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ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู…
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ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡
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ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู…
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ุจุณู…
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ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู†
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ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญ
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ุฅูŠุด ุฃู†ุชูˆุง ุนุงูŠุฒูŠู†ุŸ ุงุนู†ูŠ ุงุฏูŠู†ูŠ ุณุคุงู„ ู…ุญุฏุฏ ุงูุถู„ ุงูŠู‡
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ุจู‚ู‰ ุฃูˆ ุงู†ุง ู…ู…ูƒู† ุงุดุชุฑูŠ ู…ู† ุงู„ุฃูˆู„ ู…ู† ุงู„ุฃูˆู„ .. ู…ู†
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ุงู„ุฃูˆู„ .. ูŠุนู†ูŠ practice ..
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ู…ุงุดูŠ ุจุดูˆู ูƒุฏู‡ ุงู† ุดุงุก ุงู„ู„ู‡ ู„ุฃ ู‡ุจุฏุฃ question number
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one ุฃู†ุง ุจุฏูŠ ุฃู‚ุฑุง ุงู„ุณุคุงู„ ุฃูู‡ู…ูƒ ุงู„ู…ุนู†ู‰ ุชุจุนู‡ูˆ ุงุนุฑููƒ
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ุงูŠุด ุงู„ keyboards ุงู„ู„ูŠ ุงุญู†ุง ุนุงูŠุฒูŠู†ู‡ุง ูŠุนู†ูŠ ูƒู„ู…ุงุช
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ุงู„ู…ูุชุงุญูŠุฉ ุงู„ู„ูŠ ู…ู† ุฎู„ุงู„ู‡ุง ุจุนุฑู ุงู„ุญู„ ูˆ ุจุนุฏูŠู† ุจู‚ุฏุฑ
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ุงุดูŠู„ ุฅุฌุงุจุงุช ู…ุด ุตุญูŠุญุฉ ูˆ ุชู… ุนูŠุฏู†ูŠ ู…ู…ูƒู† ุฅุฌุงุจุฉ ุงูˆ
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ุชู†ุชูŠู† ู‡ู…ุง ุงู„ุตุญ ูุจุฎุชุงุฑ ุงู„ correct answer ุงู„ sample
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distribution describe distribution of ุงุญู†ุง ุฃุฎุฏู†ุง
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ู‚ุจู„ ู‡ูŠูƒู… ุงู„ sample distribution ุจูŠุนู…ู„ distribution
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ู„ statistic ุงู…ุง ู‡ูŠูƒูˆู† ุงู„ sample meanุฃูˆ ุงู„ู€ sample
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of proportion ุฏูŠ ุดุฑุญ ุฎุจุท ุจูŠู†ู‡ ูˆุจูŠู† ุงู„ hypothesis
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ุงู„ hypothesis ุจูŠูƒูˆู† ุงู„ claim about the population
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parameter ู‡ู†ุงูƒ ุฅุฐุง ุงู†ุชุดุฑุช ุชุณุนุฉ ูƒู„ู…ุฉ ุนู† ุงู„
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population parameter ูŠุนู†ูŠ ุจุชูƒู„ู… ุนู† ุงู„ ู…ูŠูˆ ูˆุนู†
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ุงู„ุจูˆุนูŠููŠ ุงู„ุญู„ู‚ุฉ ุงู„ุณุงุจุนุฉ ุนู†ุฏู…ุง ู†ุชุญุฏุซ ุนู† ู…ุฌู…ูˆุนุฉ
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ู…ุฌู…ูˆุนุฉ ู†ุญู† ู†ุชุญุฏุซ ุนู† ู…ุฌู…ูˆุนุฉ ู…ุฌู…ูˆุนุฉ
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ุงู„ุงุณุชุงุชูŠุณุชูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒ
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both parameters and statistics ุทุจุนุง ู„ุฃ ูุงู„ุชุงู„ูŠ
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correct answer is C ุฅุฐุง ุงู„ first one C is correct
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I just want to double check if the answers I mean
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answer key is correct or not at the end of your
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book ุญู†ุชุฃูƒุฏ ุฅูŠู‡ ุจุณ ุตุญูŠุญ ูˆู„ุง ู„ุฃ ุงู„ correct answer
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is C which is correct number two true or .. ุฅุฐุง
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one C number two true or falseุงู„ู€ Sample
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Distribution is defined as a probability
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distribution of sample sizes that can be observed
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from a given population ุฑู‚ู… ุงุชู†ูŠู† ู…ุฑุฉ ุชุงู†ูŠุฉ ุงู„ู€
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Sample Distribution is defined as a probability
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distribution of possible sample sizes that can be
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observed ู‡ูˆ ุงู„ู€ Sample Distribution ูŠุนุทูŠุจูŠุนุทูŠู†ูŠ
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ุงู„ู€ mean ุงู„ู„ูŠ ู‡ูˆ ุงู„ู€ center ุจูŠุนุทูŠู†ูŠ ุงู„ spread
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ุจูŠุนุทูŠู†ูŠ ุงู„ shape ูุจุงู„ุชุงู„ูŠ ุงู† ู‡ูˆ .. ู‡ูˆ ุจูŠุญูƒูŠ ุชุนุฑูŠูู‡
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ุนุจุงุฑุฉ ุนู† probability of distribution ุทุจุนุง ู„ุฃ ู‡ูˆ
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ุจูŠุนุทูŠ ุงู„ center ุงูˆ ุงู„ spread ุงูˆ ุงู„ shape ูุจุงู„ุชุงู„ูŠ
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ุจูŠุนุทูŠุด probability ูƒ .. ู„ู…ุง ุจุญูƒูŠ ู„ูƒ ุงู„ X bar ุจุณูˆุงุฉ
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ุฎู…ุณูŠู† ู‡ู„ ุจูŠุนุทูŠู†ูŠ probability ู„ุฃ ุงุนุทุงู†ูŠ ุงู„ center
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ุชุจุนู‡ุง ุจุณูˆุงุฉ ุฎู…ุณูŠู† ูˆุงุถุญุŸ ุฅุฐุง ู„ู…ุง ุจุญูƒูŠ send
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distribution of X barุงู„ู‚ูŠู… ู‡ูˆ 16 ุฅุฐุง ูƒุงู†ุช ุงู„ู‚ูŠู…
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ุงู„ุตุญูŠุญุฉ 10 ู…ุงุนุทุงู†ูŠุด ุงู„ุจุฑุงุจูŠุฑูŠุง ุชุจุนู‡ุง ุชุนุทุงู†ูŠ ุงู„ู‚ูŠู…
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ู„ู„ู‚ูŠู… ุฃูˆ ุงู„ู‚ูŠู… ุงู„ุตุญูŠุญุฉ ุฃูˆ ุงู„ุดูƒู„ ู†ูุณู‡ุง ุฅุฐู† ุจูŠ is
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the correct answer ุฅุฐู† ุงุชู†ูŠู† ุจูŠ ุฑู‚ู… ุชู„ุงุชุฉ ุงู„ุชู„ุงุชุฉ
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ุจูŠุญูƒูŠ amount of time it takes to complete an
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examination has left skewed distributionุงู„ุฒู…ู† ุงู„ู„ูŠ
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ู„ุงุฒู… ุนุดุงู† ุชุญุณุจ it takes a complete examination
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ุชุฎู„ุต ุงู„ุงู†ุชุญุงู† ุฅูŠู‡ ุงู„ู„ูŠ ู‡ูˆ left skewedุŸ ุชูˆุฒูŠุน ู…ุด
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normal ุฅูŠู‡ ุงู„ู„ูŠ ู‡ูˆ ู„ูŠุดุŸ left skewed with a mean of
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65 minutes and standard deviation of 8 minutes if
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64 students were randomly sampled ุฃุฎุฏ ุนูŠู†ุฉ ูƒุจูŠุฑุฉ
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ูˆู„ุง ุตุบูŠุฑุฉุŸูƒุจูŠุฑุฉุŒ ุชุฐูƒุฑ ุงุญู†ุง ุญูƒูŠู†ุง ู„ู…ุง ุชูƒูˆู† ุนู†ุฏู‡ for
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most distributions ู„ู…ุง n is large, large enough it
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means greater than 30 then we can assume the
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popularly standard distribution of the standard
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mean is approximately normally distributedู„ูˆ ูƒุงู†ุช
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N ุฃูƒุจุฑ ู…ู† 30 ูˆุญูƒูŠู†ุง for fair distribution ู„ูˆ ูƒุงู†ุช
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N ุฃูƒุจุฑ ู…ู† 15 ููˆุงุถุญ ุงู„ุญุงู„ุฉ ุงู„ู„ูŠ ุนู†ุฏู‡ left skewed ูˆ
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ุงู„ sample size ุฃุฎุฏุช ุฃุฏูŠุงุด 64 ูŠุนู†ูŠ ุนุฏุงุฏู‡ุง ุฃูŠุงุด more
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than 30 more than 30 ุฅุฐุง we are okay we are sample
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00:05:23,800 --> 00:05:26,960
the probability that the sample mean of the sample
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00:05:26,960 --> 00:05:30,740
distribution exceeds 71 minutes is approximately
75
00:05:30,740 --> 00:05:37,660
zeroูˆุงู„ู„ู‡ ู„ุฎุจุทู†ุง ู‡ูŠูƒ ูŠุนู†ูŠ ุงู†ุง ูƒู†ุช ู‡ููƒุฑ ุณูˆุงุก ููŠ
76
00:05:37,660 --> 00:05:41,280
ุงุชุฌุงู‡ ุงู†ู‡ ูŠู‚ูˆู„ูŠ ุงู„ุชูˆุฒูŠุน ุทุจูŠุนูŠ ูˆู„ุง ู„ุฃ ุทู„ู‚ ุจูŠุญูƒูŠ ู„ุฃ
77
00:05:41,280 --> 00:05:45,340
ู‡ูˆ ุนุงูŠุฒ ุงู„ mean ู„ุญุธุฉ ู…ุด ุจูŠุญูƒูŠ ุงู†ุง ู‡ุฐุง ู„ุฎุจุทูƒ ุฎุงุฑุฌ
78
00:05:45,340 --> 00:05:49,160
ุจุฏูˆู„ ุงู„ probability ุจุชุฑูƒุฒ ููŠ ุงู„ุฃูˆู„ ุงู„ X bar ุงู„ ู‡ูˆ
79
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approximately normal ู…ุธุจูˆุทุŸ ู…ุชูู‚ูŠู† ุนู„ูŠู‡ุง normal
80
00:05:52,480 --> 00:05:57,660
distributed ู…ุชูู‚ูŠู† ุนู„ูŠู‡ุง ุจุณ ุญูƒุงู„ูŠ with mean ู‚ุฏุงุดุฑ
81
00:05:57,660 --> 00:06:06,980
65 ู…ุธุจูˆุทุŸ ูˆ ุงู„ sigmaุทุจ ุฅูŠุด ูƒุงู† ุนุงูŠุฒุŸ ู„ุจุฑูˆุงุจูŠู„ุชูŠ ุฅู†
82
00:06:06,980 --> 00:06:14,020
ุณุงู… ุจุงู„ู…ูŠู† ู…ุงู„ูˆ ุงูƒุณูŠุฑ ุงู„ 71 ูˆู…ุง ุจูŠุญูƒูŠ ุงู„ุฌูˆุงุจ ุฅูŠุด
83
00:06:14,020 --> 00:06:21,800
ุจูŠุณุงูˆูŠ ุจูŠุชุฃูƒุฏ ู‡ู„ ุงู„ุฌูˆุงุจ ุจูŠุณุงูˆูŠ ุตูุฑ ูˆู„ุง ู„ุฃ ุจูŠุญู„
84
00:06:21,800 --> 00:06:25,180
ุงู„ู…ุซู„ุฉ ุฃู†ุง ุตุฑุช ู…ุด ุจุฑุญู„ ุงู„ู…ุซู„ุฉ ุฃู†ุง ูƒู†ุช ูุงูƒุฑ ุฃุญูƒูŠ
85
00:06:25,180 --> 00:06:30,800
ุงู„ุชูˆุฒูŠุน ุงู„ุทุจูŠุนูŠ ูˆู„ุง ู„ุฃ ุจุญุงูˆู„ูŠ ุนู„ู‰ ุงู„ Z ู…ุธุจูˆุท ุงู„ CZ
86
00:06:30,800 --> 00:06:37,430
ุฃูƒุจุฑ ู…ู† 71 minus the meanover sigma 8 ุนู„ู‰ square
87
00:06:37,430 --> 00:06:42,570
root ู„ู„ N ุงู„ N ูƒุฏู‡ุŸ 64 ู‡ูˆ ุฃุนุทุงูƒ ุฅูŠุงู‡ุง ุนุดุงู† ุฃุนุฑู
88
00:06:42,570 --> 00:06:46,350
ุฃุทู„ุน ู…ูŠู†ุŸ ุฃู‡ ุจุงู„ุธุจุท ุนุดุงู† ุฃุนุฑู ุฃุทู„ุน ุงู„ square root
89
00:06:46,350 --> 00:06:54,430
ุชูƒูˆู† ู…ุซู„ุง ุจุฏูŠู‡ุงุด calculator ู‡ุฐุง ุฅูŠุด ู‡ุชุณุงูˆูŠุŸ
90
00:06:54,430 --> 00:07:01,010
ู‡ุฏูˆู„ ุงู„ุจุตุด ู…ูˆุฌูˆุฏุŸsix ุจุนุฏูŠู† ุชู…ุงู†ูŠุฉ ุน ุชู…ุงู†ูŠุฉ ู…ุด ู‡ูŠูƒ
91
00:07:01,010 --> 00:07:07,690
ูŠุนู†ูŠ ุจุฏูˆุฑ ุนู„ู‰ P of Z ุฃูƒุจุฑ ู…ู† ุณุชุฉ Z ุฃูƒุจุฑ ู…ู† ุณุชุฉ ุงู‡
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00:07:07,690 --> 00:07:12,730
ูˆุงุญุฏ ุจูŠุทู„ุน ูˆุงุญุฏ ู†ู‚ุต ูˆุงุญุฏ ูˆุงุญุฏ ู†ู‚ุต ุณูŠ ุงู‡ ู‡ุงูŠ ุงู„ุณุชุฉ
93
00:07:12,730 --> 00:07:18,600
ุงู„ุณุชุฉ ูˆูŠู† ุงู„ white side ุนู„ู‰ ููˆู‚ ุงู„ุนู„ุจูŠุฉุงู„ู€ tab
94
00:07:18,600 --> 00:07:21,740
ุงู„ู…ุนุทู‰ ุงู„ area ู„ูˆูŠู†ุŸ to the left ุทุจุนุง z ุงู„ area to
95
00:07:21,740 --> 00:07:25,680
the left sideุŒ ู…ุธุจูˆุทุŸ ุงุฐุง this equals one minus b
96
00:07:25,680 --> 00:07:31,760
of z less than six ุงู„ tab ุงู„ู…ุนุทุงู†ูŠ ู„ุบุงูŠุฉ 3.4 ูˆ ุฌูˆ
97
00:07:31,760 --> 00:07:38,000
ูƒุงู† 9998 ููŠ ุงู„ุงุฎุฑุŒ ุงุฐุง ุชู‚ุฑูŠุจุง ูˆุงุญุฏุŒ ุงุฐุง ู‡ุฐู‡ ูˆุงุญุฏุŒ
98
00:07:38,000 --> 00:07:41,440
ุงุฐุง ุงู„ุฌุงู…ุนู‡ ู…ุด ุณุงูˆูŠุŒ ูŠุนู†ูŠ ุงู„ุฌุงู…ุนู‡ ุตุญุŒ ู„ุงุญุธุฉ ุงู†ุง
99
00:07:41,440 --> 00:07:44,940
ุญู„ุช ุงู„ู…ุซู„ ุงุณุชุฎุฏู…ุช calculatorูˆู„ุง ุงุณุชุฎุฏุงู… ุงู„ table
100
00:07:44,940 --> 00:07:47,980
ู‡ุงูŠ ุงู„ู„ูŠ ุงู†ุง ุนุงูŠุฒ ุงูˆุตู„ู„ูƒูŠู‡ุง ูŠุนู†ูŠ ุจู…ู…ูƒู† ุงุญู„ูŠ ู…ุซู„ุง
101
00:07:47,980 --> 00:07:53,020
.. ุทุจ ู‡ูˆ ู…ุด .. ู…ุด ู‡ูŠูƒ ู‡ุช .. ู‡ุชุงูƒู„ in 64 ุนุดุงู† ุชูƒูˆู†
102
00:07:53,020 --> 00:07:58,920
ุงู„ calculations ู…ุงู„ู‡ุงุŒ ุชูƒูˆู† ุงู„ุญุณุงุจุงุช ู…ุงู„ู‡ุงุŒ ุณู‡ู„ุฉุŒ
103
00:07:58,920 --> 00:08:04,660
ุงุฐุง ุงู†ุง ุงุดูŠ ุฌูˆุงุจุŸtrue ุฅุฐุงู‹ ุชู„ุงุชุฉ ุงู„ answer is a
104
00:08:04,660 --> 00:08:09,860
ูˆุงุถุญ ุงู„ููƒุฑุฉ ุฅุฐุง ุงู„ู…ุซู„ุฉ ุจูŠุญูƒูŠู„ูƒ ุญู„ ู…ุณุชู„ุงุช X bar
105
00:08:09,860 --> 00:08:16,160
ุฃูƒุจุฑ ู…ู† 71 ุญู„ุชู‡ุง ุจ steps ุตุบูŠุฑุฉ ุทู„ุนุช ุฌูˆุงุจ ุชู‚ุฑูŠุจุง ุจ
106
00:08:16,160 --> 00:08:20,500
0.00 ูุจุฏูŠ ูˆุงุญุฏุฉ ู…ู†ูƒู… ุชุนุทูŠู†ูŠ ู†ูุณ ุงู„ุณุคุงู„ ุจุณ ุชุทู„ุน
107
00:08:20,500 --> 00:08:25,280
ุงู„ุฌูˆุงุจ ุบู„ุท ูŠุนู†ูŠ ุบูŠุฑ ุงู„ู…ุซู„ุฉequal one ู…ู…ูƒู†
108
00:08:25,280 --> 00:08:29,260
approximately ู…ุซู„ุง ุงู‡ equal one ุงู‡ ุทุจุนุง ู„ุฃ ู‡ูŠ ุงู„
109
00:08:29,260 --> 00:08:32,740
equal one ู‡ุฐู‡ ู„ุฃู‚ู„ ู…ู† ุณุชุฉ equal one ุงู‡ ู„ุฃู‚ู„ ู„ุฃู‚ู„
110
00:08:32,740 --> 00:08:37,340
ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„
111
00:08:37,340 --> 00:08:39,760
ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„
112
00:08:39,760 --> 00:08:42,420
ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„
113
00:08:42,420 --> 00:08:43,500
ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„
114
00:08:43,500 --> 00:08:50,320
ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„
115
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ู„ุฃู‚
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00:08:54,130 --> 00:09:01,890
ุฎู„ุตู†ุง ุชู„ุงุชุฉ ุงูŠู‡ุŸ ู…ุธุจูˆุท ู‡ูŠูƒุŸ ุงูŠู‡ ุงู„ุชู„ุงุชุฉ ุงูŠู‡ุŸ ุฑู‚ู…
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00:09:01,890 --> 00:09:10,550
ุงุฑุจุนุฉ The
118
00:09:10,550 --> 00:09:15,110
distribution of the number of loaves of bread sold
119
00:09:15,110 --> 00:09:19,590
per week by large bakery over the past five years
120
00:09:19,590 --> 00:09:28,670
has a mean of7750 ู‡ุงูŠ ุงู„ู…ูŠู† ูˆุตูุฉ
121
00:09:28,670 --> 00:09:32,830
ุงู„ุดู…ุณ 1450
122
00:09:32,830 --> 00:09:39,370
ู…ูŠุฉ ูˆุฎู…ุณุฉ ูˆุงุฑุจุนูŠู† ุงุฐุง
123
00:09:39,370 --> 00:09:44,830
ูƒุงู†ุช ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏHas been
124
00:09:44,830 --> 00:09:48,810
selected what's the approximate probability that
125
00:09:48,810 --> 00:09:52,230
the mean number of loaves sold in the same brief
126
00:09:52,230 --> 00:09:59,350
sealed ู‡ูˆ ุจุญูƒูŠ ุฃูŠุด ุงู„ mean ุฎู„ูŠ ุจุงู„ูƒ is an x bar
127
00:09:59,350 --> 00:10:04,930
ุฃูƒุจุฑ ู…ู† seven thousand eight hundred ninety five
128
00:10:04,930 --> 00:10:08,430
ุจุฏูˆุง ุงู„ mean ุฅูŠุด ุจูŠุณุงูˆูŠ ู†ูุณ ุงู„ุณุคุงู„ ุฏู‡ ุจุงู„ุธุจุท
129
00:10:08,430 --> 00:10:09,370
ุญุงูˆู„ูˆุง ู„ู„ z
130
00:10:14,740 --> 00:10:26,540
minus ุงู„ mean ุนู„ู‰ ุงู„ sigma over 40 ุจุชุญู„ูŠู‡ุง ูˆ
131
00:10:26,540 --> 00:10:29,560
ุจุชุชุฃูƒุฏ ู…ู† ุงู„ุฌูˆุงุจ ุงู† ููŠ ุฌู‡ุฉ ุฏู‡ ูˆู‚ุช ููŠู‡ุง ู…ุด ู‡ูŠูƒ ู†ูุณูƒ
132
00:10:29,560 --> 00:10:35,860
ุชููƒุฑู‡ ุนุดุงู† ุถูŠู‚ุฉ ูˆ ุจูŠุญูƒูŠ ุงู„ุฌูˆุงุจ ู†ุนู… ุจุชู„ุนุจ ุตุญูŠุญ ุงุฐุง
133
00:10:35,860 --> 00:10:39,660
ุนุงูŠุฒูƒ ุงู„ base ุจุณ ุช check this result ุจุชุฃูƒุฏ ู…ู†ู‡ุง
134
00:10:39,660 --> 00:10:43,970
ุจุชุฃูƒุฏ ุงู„ุญู„ ุตุญ ูˆู„ุง ู„ุฃุฅุฐุง ูˆุงุถุญ ู†ูุณ ุงู„ secret ุงู„ุณุคุงู„
135
00:10:43,970 --> 00:10:54,490
ุชู„ุงุชุฉ ู…ุงุดูŠ ุจุณ ุฃู‚ุฑุง ุฎู…ุณุฉ ุฎู…ุณุฉ major league baseball
136
00:10:54,490 --> 00:11:04,530
salaries average 3.26 ู…ู„ูŠูˆู† ุจูŠุชูƒู„ู… ุนู„ู‰ ู…ูŠู†ุŸ ุจูŠุชูƒู„ู…
137
00:11:04,530 --> 00:11:08,230
ุนู„ู‰ ุฑูˆุงุชุจ ุชุจุนูˆู† ุงู„ .. ุงู„ baseball ุงุฐุง ุฏูˆู„ ุฑูˆุงุชุจู‡ู…
138
00:11:08,230 --> 00:11:12,450
ุถุฎู…ุฉูŠุนู†ูŠ ู„ูˆ ุฃุชุนู„ู… ู„ุนุจุฉ ุฒูŠ ู‡ูŠูƒ ูˆ ู†ูุณ ุงู„ statistics
139
00:11:12,450 --> 00:11:17,510
ูƒุงู† ุฃุญุณู† ู…ุธุจูˆุทุŸ ู‡ูˆ ุจูŠุญูƒูŠ ุฑูˆุงุชุจ ูƒุฏู‡ุดุŸ 3.26 ู…ู„ูŠูˆู†
140
00:11:17,510 --> 00:11:22,150
with standard deviation of 1.2 suppose a sum of
141
00:11:22,150 --> 00:11:27,230
hundred funds approximate ู†ูุณ ุงู„ู‚ุตุฉุŒ ุฅุฐุง ุงู„ุฎู…ุณุฉ
142
00:11:27,230 --> 00:11:34,850
similar ูˆุงุถุญุŸ ุฎู…ุณุฉ ุฒูŠ ูˆ ุชุดุฌุน ู†ุถุงูŠู‚ ูˆู‚ุช ูˆุฎู…ุณุฉ ุฌูˆุงุจ
143
00:11:34,850 --> 00:11:36,250
ุฏูŠุŒ six
144
00:11:39,150 --> 00:11:43,870
ุฎู…ุณุฉ ูˆ ุณุชุฉ ู…ุซู„ู‹ุง
145
00:11:43,870 --> 00:11:48,490
ุฎู…ุณุฉ
146
00:11:48,490 --> 00:11:52,790
ูˆ ุณุชุฉ ู…ุซู„ู‹ุง ุฎู…ุณุฉ ูˆ ุณุชุฉ ู…ุซู„ู‹ุง
147
00:12:08,580 --> 00:12:12,940
At a computer manufacturing company ุจุชูƒู„ู… ุนู„ู‰ ุดุฑูƒุฉ
148
00:12:12,940 --> 00:12:17,200
ุตู†ุงุนุฉ ุงู„ุญูˆุงุตูŠู„ The actual size of computer chips
149
00:12:17,200 --> 00:12:21,440
is normally distributed of a mean with a mean of
150
00:12:21,440 --> 00:12:29,060
one centimeter ุงู„ mean ูˆุงุญุฏ and standard deviation
151
00:12:29,060 --> 00:12:34,380
of point one a random sample of twelve
152
00:12:37,080 --> 00:12:41,500
in equal twelve ูˆู„ุญุธุฉ ูˆุญูƒู‰ ููŠ ุงู„ุฃุตู„ ุนู†ุฏู‰ ุชูˆุฒูŠุน
153
00:12:41,500 --> 00:12:44,620
ุทุจูŠุนู‰ ู…ุด ู‡ูŠูƒ ุนู„ุดุงู† ูƒุฏู‡ ุงู†ุช normal ู„ุฃู† ุงู„ in is
154
00:12:44,620 --> 00:12:47,840
small in this case to solve the problem we have to
155
00:12:47,840 --> 00:12:50,280
assume the population is normal otherwise you
156
00:12:50,280 --> 00:12:56,180
can't continue because we in chapter seven we are
157
00:12:56,180 --> 00:13:00,510
talking about if in is large enoughthen the sample
158
00:13:00,510 --> 00:13:03,590
sizes doesn't matter ู…ุด ู…ุดูƒู„ุฉ ุญุฌู… ุงู„ุนูŠู†ุฉ ู„ูƒู† ู„ู…ุง
159
00:13:03,590 --> 00:13:07,810
ุชูƒูˆู† n ุตุบูŠุฑุฉ ุงู„ sample size ุจูŠูƒูˆู† ู…ู‡ู… ุฅุฐุง ุงู„ุญูƒุงูŠุฉ
160
00:13:07,810 --> 00:13:12,010
ุชุญูƒูŠู„ูŠ ุทุจูŠุนูŠ ุจุชุฑูŠุญูƒ n equal to twelve ูˆ ุจุตุฏุฑ
161
00:13:12,010 --> 00:13:15,970
ุจุฑู†ุงู…ุฌ ุงู„ ุงู„ sample mean will be below ุงู„ mean
162
00:13:15,970 --> 00:13:22,150
will be below 9.95 ุจู†ูุณ
163
00:13:22,150 --> 00:13:27,830
ุงู„ููƒุฑุฉ ูŠุนู†ูŠ ู‡ุฐุง ุงู„ุญุงู„ุฉ ุชุจู‚ู‰ ุจุญุงูˆู„ ู„ุฒูŠูƒู„ู‡ู… minus
164
00:13:27,830 --> 00:13:33,030
ูˆุงุญุฏ minus ูˆุงุญุฏ ูˆุนู„ู‰ ุงู„ sigma over square root of
165
00:13:33,030 --> 00:13:37,530
twelve ู†ูุณ ุงู„ููƒุฑุฉ ุงู„ู„ูŠ ูุงุชุช ููŠ ุงู„ุณุคุงู„ ุงู„ุณุงุจุน
166
00:13:37,530 --> 00:13:42,250
ุงู„ุฌูˆุงุจ ุชุจุนู‡ ุณุงู„ุจ ู‡ุงู†ุจูˆู†ุช ุงู„ู„ู‡ ูŠุณุงู…ุญู†ูŠุŒ ู…ูŠู† ุญูƒุช
167
00:13:42,250 --> 00:13:46,710
ุณุงู„ุจุŸ ุณุงู„ุจุŸ ูƒุงู†ุช ุนุฒุงุฌุฉุŸ ู…ุด ุฏูˆุฑุงุจูŠู„ุฉ ุณุงู„ุจุŒ ุงู†ุช
168
00:13:46,710 --> 00:13:55,610
ุนุฒุงุฌุฉุŸ ุงู‡ ุงู‡ ุงู‡ ุงู‡ุฃู†ุง ู…ุงุจุญูƒูŠ ุฌูˆุงุจุด ุจุณุงูˆุฉ ูƒู„ู‡ุงุŒ ูƒุฏู‡
169
00:13:55,610 --> 00:14:02,150
ุฃู‚ู„ ู…ู† ุงู„ุณู†ุฉ ุชู‚ุฑูŠุจุง zero ุงู†ุง ุณุคุงู„ ุงูŠุดุŸ zero ุงุฑุจุน
170
00:14:02,150 --> 00:14:07,950
ูˆุงุญุฏ ุชู‚ุฑูŠุจุง ู‡ูŠูƒ ุดูˆู ุฏุงูŠู…ุง ุงู„ probability positive
171
00:14:07,950 --> 00:14:09,930
between zero and one ูŠุนู†ูŠ ู„ูˆ ุงู†ุง ุจุญู„ ู…ุซู„ุง ุทู„ุนุช
172
00:14:09,930 --> 00:14:13,250
negative ู…ุซู„ุง ุงู„ู„ูŠ ุฌุงุจุช ุบู„ุท ู„ูˆ ุทู„ุนุช ุงูƒุชุฑ ู…ู† ูˆุงุญุฏ
173
00:14:13,250 --> 00:14:16,330
ุงู„ู„ูŠ ุฌุงุจุช ุจุฑุถู‡ ุบู„ุท ู„ุงุฒู… ุชูƒูˆู† between zero and one
174
00:14:16,330 --> 00:14:17,810
ุณุคุงู„ ุชู…ุงู†ูŠุฉ
175
00:14:25,260 --> 00:14:28,980
ุงู„ุชู…ุงู†ูŠุฉ ุจูŠุญูƒูŠ the owner of a fish market has an
176
00:14:28,980 --> 00:14:36,420
assistant ุจูŠุญูƒูŠ owner ู„ fish market ุตุงุญุจ ู…ุญู„ ู„ุจูŠุน
177
00:14:36,420 --> 00:14:41,980
ุงู„ุฃุณู…ุงูƒ has assistant who has determined that the
178
00:14:41,980 --> 00:14:45,620
weights of catfish are normally distributed with a
179
00:14:45,620 --> 00:14:47,240
mean of 3.2
180
00:14:50,800 --> 00:14:57,880
mean of 3.2 pound and standard deviation of 0.8 if
181
00:14:57,880 --> 00:15:02,340
a sample of 64 fish yields ุงุชุฏุงู†ูŠ ุงู„ sample size
182
00:15:02,340 --> 00:15:08,060
64 fish yields a mean of 3.4 pound ู‡ุฏูˆู„ ูŠุนุทูˆ ู…ู†
183
00:15:08,060 --> 00:15:14,720
ู…ูŠู† ู‡ุฏูˆู„ ูŠุนู†ูŠ ุงู„ sample ู…ู† ู…ูŠู† ุชุจุนู‡ู… 3.4 ุฅุฐุง
184
00:15:14,720 --> 00:15:18,980
ุฃุฎุฏ sample of 64 fish yields a mean of 3.4 pound
185
00:15:20,720 --> 00:15:23,140
ุจุณุฃู„ what's the probability of obtaining a sample
186
00:15:23,140 --> 00:15:27,460
mean this large or largerุŸ ุฅูŠุด ุงุญุชู…ุงู„ ุฃุญุตู„ ุนู„ู‰
187
00:15:27,460 --> 00:15:31,920
sample mean ู‡ุฐุง ุงู„ู‚ูŠู…ุฉ ุฃูˆ ุฃูƒุจุฑ ู…ู†ู‡ุงุŸ ูŠุนู†ูŠ X bar
188
00:15:31,920 --> 00:15:38,080
ู…ุงู„ู‡ ุฃูƒุจุฑ ู…ู†ู‡ุงุŸ ู‡ูŠ ุฃูˆ ุฃูƒุจุฑุŸ ุจุณุŒ ูˆ ุงู„ุญู„ ุจูŠุตูŠุฑ ุดุบู„
189
00:15:38,080 --> 00:15:47,300
ุนุงุฏู‰ุŒ ู†ุธุจุทุŸ ูู‡ุฐุง ู‡ุชุณุงูˆูŠ P of Z ู‡ุงูŠ ุงู„ mean minus
190
00:15:48,460 --> 00:15:55,800
3.2 over sigma over square root of 64 ู‡ุฐู‡
191
00:15:55,800 --> 00:15:59,880
ุงู„calculations ุนุงุฏุฉ ุณู‡ู„ุฉ ุทุจุนุง ููŠ ุงู„ .. ู‡ู†ุง ููŠ
192
00:15:59,880 --> 00:16:04,560
point 2 ู…ุด ู‡ูŠูƒ ูˆ ุงู„ู„ูŠ ุชุญุช ุดูˆ ุณุงูˆูŠ point 8 ุนู„ู‰ 8
193
00:16:04,560 --> 00:16:15,900
ูŠุนู†ูŠ ู‡ุฐุง point 8 ุนู„ู‰ 8 ูŠุนู†ูŠ ูŠุนู†ูŠ ุจูŠุตูŠุญุด .. ุงูŠุด
194
00:16:15,900 --> 00:16:22,240
ุจุงู„ุฌูˆุงุจ ุงุทู„ุน ู‡ู†ุงุŸpoint 8 ุน 8 ูƒุฏู‡ุŸ
195
00:16:22,240 --> 00:16:29,400
ู„ุฃ ุจุถุญูƒ ุจุณ point 8 ุน 8 ู„ุฃูˆู„ point 8 ุน 8 ูŠุนู†ูŠ point
196
00:16:29,400 --> 00:16:33,320
1 ู…ู† 10 ูˆุงุญุฏ ู…ู† ุนุดุฑุฉ ุดูˆู ู‡ุงูŠ ุงู„ุฃุฎุทุงุฑ ู…ู…ูƒู† ุชุฌุฑุฃ ูƒุฏู‡
197
00:16:33,320 --> 00:16:37,900
ููŠ ู†ูุณูƒ point 1 ุทุจุนุง point 8 ุน 8 ุทุจุนุง ุฃูˆู„ ู…ุง
198
00:16:37,900 --> 00:16:42,080
ุจุดูˆูู‡ุง ููŠู‡ุง point 1 ูˆ ู‡ุฐุง ุบู„ุท ู„ูŠุด ุชู…ุงู†ูŠุฉ ู…ู† ุนุดุฑุฉ ูˆ
199
00:16:42,080 --> 00:16:45,080
ูˆุงุญุฏ ู…ู† ุนุดุฑุฉ ู‡ุฐุง ุชู…ุงู†ูŠุฉ ู…ู† ุนุดุฑุฉ ุน ุชู…ุงู†ูŠุฉ ุฅูŠุด
200
00:16:45,080 --> 00:16:54,760
ุงู„ุฌูˆุงุจ point 1 point 11 ู…ู† 10 ูŠุนู†ูŠ ูŠุนู†ูŠ ูˆุงุญุฏ
201
00:16:54,760 --> 00:16:57,840
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
202
00:16:57,840 --> 00:17:01,480
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
203
00:17:01,480 --> 00:17:01,480
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
204
00:17:01,480 --> 00:17:01,620
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
205
00:17:01,620 --> 00:17:01,660
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
206
00:17:01,660 --> 00:17:02,560
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
207
00:17:02,560 --> 00:17:02,960
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
208
00:17:02,960 --> 00:17:03,840
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
209
00:17:03,840 --> 00:17:04,960
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
210
00:17:04,960 --> 00:17:15,400
ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ ู…ู† ุนุดุฑ ูŠุนู†ูŠ ูˆุงุญุฏ
211
00:17:15,400 --> 00:17:21,650
ู…ู† ุนุดุฑ ูŠุนู†ูŠุฒูŠ ุงู‚ู„ ู…ู† ุงุชู†ูŠู† ุนู†ุฏ ุงู„ุงุชู†ูŠู† ุงูŠุด ุฌูˆุงุจ
212
00:17:21,650 --> 00:17:29,870
ุจุทู„ุน ู‡ุฐุง ุณุคุงู„ ุฑู‚ู… ุชู…ุงู†ูŠุฉ ุทู„ุน
213
00:17:29,870 --> 00:17:38,210
ุงู„ table ุนู†ุฏ ุงู„ุงุชู†ูŠู† ุชุณุนุฉ
214
00:17:38,210 --> 00:17:42,430
ุณุจุนุฉ ุณุจุนุฉ ุงุชู†ูŠู† ู…ุธุจูˆุท ุงุฐุง point nine seven seven
215
00:17:42,430 --> 00:17:47,080
twoone minus ูŠุนู†ูŠ zero, two, two, eight ู…ุด ู‡ูŠุŸ
216
00:17:47,080 --> 00:17:51,200
ูุจุชุงู„ูŠ ุฅูŠุด ุงู„ุฌูˆุงุจ ุชุจุนูŠู‡ุŸ ุฅุฐุง ุจูŠู‡ is the correct
217
00:17:51,200 --> 00:17:55,980
answer ุดูˆู
218
00:17:55,980 --> 00:18:01,260
ุชุฃูƒุฏ ู„ูˆ ุญุงุทุทุชู„ูƒ ุฅุฌุงุจุงุช ุชู„ุงุชุฉ ุจุชูƒูˆู† ูˆุงุญุฏุฉ ู…ู†
219
00:18:01,260 --> 00:18:05,360
ุงู„ุฃุฎุทุงุก ู…ู…ูƒู† ุฃู‚ุน ููŠู‡ุง ู‡ู†ุง ูŠุนู†ูŠ ุฃูŠ ุญุงุฌุฉ ุบู„ุทุช ุงู„ุญุณุงุจ
220
00:18:05,360 --> 00:18:10,440
ู‡ูŠุทู„ุนู„ูƒ ูˆุงุญุฏุฉ ู…ู† ู‡ุฏูˆู„ ูุงู†ุช ุฑูƒุฒูŠ ุดูˆูŠุฉ ุณุคุงู„ ุชุณุนุฉ
221
00:18:13,730 --> 00:18:17,990
true or false if the amount of gasoline purchased
222
00:18:17,990 --> 00:18:22,110
per car at large surface stations has a population
223
00:18:22,110 --> 00:18:28,090
of 15 gallons and population deviation of 4
224
00:18:28,090 --> 00:18:36,410
gallons then 99.73 of all cars
225
00:18:44,460 --> 00:18:49,240
ูˆุงู„ุจุฑุด is between 3 and 27 gallons ุงู‡ ุจุฏู†ุง ู†ุญู„ู‡ุง
226
00:18:49,240 --> 00:18:55,660
ุงู†ุง ุจุฏูŠ ุญุฏ ุญู„ ุงู„ุงุณุฆู„ุฉ ุจุชุฐูƒุฑูˆุง ุงู„ empirical rule ุงู„
227
00:18:55,660 --> 00:19:01,660
empirical rule ูƒุงู† ูŠุญูƒูŠ ุงูŠุด ูƒุงู† 689599.7 of the
228
00:19:01,660 --> 00:19:07,780
data will fall within ุงู„ุงุฎูŠุฑ within three standard
229
00:19:07,780 --> 00:19:12,020
deviation of the population mean ุจุณ ู‡ู†ุง ุฃู†ุง ุนู†ุฏู‰
230
00:19:12,020 --> 00:19:19,170
ุจุชูƒู„ู…ุด ุนู„ู‰ ุงู„ ..ุน ุงู„ X ุจุงุฑ ูƒู†ุง ู†ุญูƒูŠ ุงุญู†ุง ุงูŠุด ู„ูˆ ุงู„
231
00:19:19,170 --> 00:19:24,210
ู…ูŠูˆ ู…ุงู†ุณ ุซุฑูŠ ุณูŠุฌู…ุง ูˆ ู…ูŠูˆ ุจู„ุณ ุซุฑูŠ ุณูŠุฌู…ุงุŒ ู…ุธุจูˆุทุŸ ุจุณ
232
00:19:24,210 --> 00:19:30,010
ุฏู‡ ู…ุด ุณูŠุฌู…ุง ุงู„ุนุงุฏูŠุฉุŒ ุจุญูƒูŠ ุน ุงู„ X ุจุงุฑ ุงู„ู„ูŠ
233
00:19:30,010 --> 00:19:32,370
ุงู†ุช ู„ุงุญุธุด ุจูŠุญูƒูŠ ู‡ูˆ ุงู„ probability of obtaining
234
00:19:32,370 --> 00:19:36,790
sample mean ุงูˆ ุตุบูŠุฑ then 997 of all cars will
235
00:19:36,790 --> 00:19:44,280
purchase between 3 27ูˆู‡ู†ุง ุงุนุทุงู†ูŠ ุงูŠุดุŸ ู‡ุงูŠ ุงู„ุฎู…ุณุชุงุด
236
00:19:44,280 --> 00:19:49,500
ู‡ุฐูˆู„ ู…ูŠู† ุชุจุนู‡ู… ุงุฐุง ุนู†ุฏูŠ ุงู…ุง ุงุญู†ุง ุจุฏูŠ ุงุญู„ู‡ุง ู…ูŠูˆ
237
00:19:49,500 --> 00:19:53,200
ู…ุงูŠู† ุซุฑูŠ ุณูŠุฌู…ุง ู…ูŠูˆ ุจู„ุงุณุชุฑูŠ ุณูŠุฌู…ุง ุฎู„ูŠู†ูŠ ุงุจุฏุฃ
238
00:19:53,200 --> 00:20:01,440
ุจุงู„ุชุงู†ูŠ ูŠุนู†ูŠ ุงู„ู…ูŠู† ุงูŠุด ุจูŠุณุงูˆูŠุŸ ุงู„ู…ูŠู† ุฎู„ุงุดุŸ ูƒุฏู‡ุŸ
239
00:20:01,440 --> 00:20:05,800
ุฎู„ูŠู†ูŠ ุงุญู„ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ูŠู† ู‚ุฏุงุดุŸ ู†ู‚ุต ุชู„ุงุชุฉ ููŠ ุฃุฑุจุนุฉ
240
00:20:05,800 --> 00:20:10,510
ู…ุด ู‡ูŠูƒุŸ ูˆุฎู…ุณุชุงุด ุฒูŠ ุชู„ุงุชุฉ ููŠ ุฃุฑุจุนุฉู…ุด ุจุทู„ุน ุงู„ุฌูˆุงุจ
241
00:20:10,510 --> 00:20:15,870
ู‡ู†ุง ุชู„ุงุชุฉ ุงูˆ ู‡ู†ุง ุงุฐุง
242
00:20:15,870 --> 00:20:19,250
ุจุทู„ุน ู…ู† ู‡ู†ุง ุงู„ู‰ ุงูŠู†ุŸ ู…ู† ุงู„ุชู„ุงุชุฉ ู„ุบุงูŠุฉ ุงู„ุณุงุจุนุฉ
243
00:20:19,250 --> 00:20:25,570
ูˆุนุดุฑูŠู† ุณุจุนูŠู† ู…ู…ูƒู† ู‡ุฐู‡ ู†ุญูŠู„ู‡ุง ุนู„ู‰ ุงู„ probability
244
00:20:25,570 --> 00:20:27,150
ุงู„ุนุงุฏูŠุฉ ุงู‡ ู…ู…ูƒู† ุชุญูŠู„ู‡ุง ุนู„ู‰ ุงู„ probability ุงู„ุนุงุฏูŠุฉ
245
00:20:27,150 --> 00:20:34,530
ุงู„ุฌูˆุงุจ ุทู„ุน ุนู„ู‰ ู‡ุฐู‡ ู‡ู†ุง ูุงู„ุฌูˆุงุจ ูƒุฏู‡ุŸ ุชู„ุงุชุฉ ู„ุณุจุนุฉ
246
00:20:34,530 --> 00:20:40,130
ูˆุนุดุฑูŠู† ู‡ุฐุง ุงู„ุณุคุงู„ ูƒุฏู‡ุŸ ุณุคุงู„ ุชุณุนุฉ ุชุณุนุฉู„ูˆ ุทู„ุนุช ุนู„ู‰
247
00:20:40,130 --> 00:20:43,670
ุงู„ูƒุชุงุจ ุจูŠุญูƒูŠู„ูŠ ุฌูˆุงุจ false ุทูŠุจ ู‡ูˆ ุจูŠุทู„ุน ู†ูุณ ุงู„ุฌูˆุงุจ
248
00:20:43,670 --> 00:20:48,550
ู…ุน ูƒุฏู‡ ุงู„ูƒู„ุงู… ู…ุด ุตุญ ุงู„ู„ูŠ ุฃู†ุง ุนู…ู„ุชู‡ ู„ูŠุดุŸ ู‡ูˆ ุจูŠุชูƒู„ู…ุด
249
00:20:48,550 --> 00:20:51,490
ุนู„ู‰ ุงู„ .. ุนู„ู‰ ุงู„ except ูƒู„ุงู… ุนู„ู‰ ุงู„ except
250
00:20:51,490 --> 00:20:56,750
ูุจุงู„ุชุงู„ูŠ ุฅูŠุด ู‡ุชุตูŠุฑุŸ ุบู„ุท ู‡ุฐุง ุบู„ุท ู‡ุฐุง ุงู„ุทุฑูŠู‚ุฉ ู…ุด ุตุญ
251
00:20:56,750 --> 00:21:01,710
ุงู‡ ูŠุนู†ูŠ ุงุญู†ุง ุงู„ุตุญูŠุญ ุงูŠู‡ ู„ุงู† ู†ุทู„ุน ุงู„ .. ุงู„ sigma x
252
00:21:01,710 --> 00:21:06,130
ู…ุงุฑูŠุด ุจุงู„ุณุงูˆูŠุฉ ุงู‡ ุทุจุนุง ุตุญ ุงู†ุง ุทุจุนุง ุทุจุนุง ุงู†ุง ุทุจุนุง
253
00:21:06,130 --> 00:21:12,000
ุทุจุนุง ุทุจุนุง ุทุจุนุง ุทุจุนุงุงู„ุงู† ู…ุด ู…ุชุณุงูˆู‰ ููŠ ุงู„ู…ุซู„ุฉ ุงู„ุงู†
254
00:21:12,000 --> 00:21:18,700
ุฎู„ุงุต ู‡ู„ ููŠ ุงู† ู…ูˆุฌูˆุฏุŸ ู„ุง ู…ุงุนุฑู ุงูƒูŠุฏ ู…ุด ู‡ู‚ุฏุฑ ุงุญู„ ู‡ุฐู‡
255
00:21:18,700 --> 00:21:22,700
ุทูŠุจ ุฅุฐุง ุงู„ู…ุนู†ู‰ ูƒุฏู‡ ุงู„ูƒู„ุงู… ุงู„ู„ูŠ ุญูƒุงู„ูŠู‡ ุตุญ ูˆู„ุง ุบู„ุทุŸ
256
00:21:22,700 --> 00:21:26,600
ุบู„ุท ู‡ู„ ุจุชู‚ุฏุฑ ุงู†ุช ุงู„ุขู† ุชุญู„ูŠ ุงู„ู…ุซู„ุฉ ุจุงู„ู‚ูˆุงู†ูŠู†
257
00:21:26,600 --> 00:21:31,900
ุงู„ุนุงุฏูŠุฉุŸ ู„ุง ู…ุณุชุญูŠู„ ู…ุด ู‡ู‚ุฏุฑ ุงุญู„ ู‡ุฐู‡ ุงู„ูƒู„ุงู…ุŸ ุฃูŠ
258
00:21:31,900 --> 00:21:37,640
probabilityุŸ
259
00:21:39,170 --> 00:21:46,670
ุงู„ู„ูŠ ุฃู†ุง ุจุชุทู„ุน ุงู„ probability ู„ู…ูŠู†ุŸ ู„ู„ X ูŠุนู†ูŠุŸ
260
00:21:46,670 --> 00:21:55,890
ุตุญ ุทู„ุนูŠู† ุฃู‡ ุตุญ ููƒุฑุง ู…ุด ููƒุฑุง ุบู„ุท ุฅุฐุง ุงู„ุฌูˆุงุจ ุบู„ุท ู„ุฅู†
261
00:21:55,890 --> 00:21:58,390
ุงู„ุทู„ุงู‚ ู‡ูŠ ูƒุชุงุจุชุงู† ูŠุนู…ู„ ูŠุนู†ูŠ ุจูŠุตูŠุฑ ุงู„ probability
262
00:21:58,390 --> 00:22:06,330
ุชู„ุงุชุฉ ุฃู‚ู„ ู…ู† X ุฃู‚ู„ ู…ู† 27 ุจูŠุตูŠุฑ ุชู„ุงุชุฉ ู†ู‚ุต ู„ู…ูŠู†ุŸ
263
00:22:08,550 --> 00:22:11,910
ุนู„ู‰ ุงู„ู€ Sigma ู‡ุฐุง ุงูŠุดุŸ ุฎู„ู‘ูŠ ุจุงู„ูƒ ู‡ูˆ ุงู„ู„ูŠ ุจูŠุญูƒูŠ ..
264
00:22:11,910 --> 00:22:18,950
ุงู„ุฌูˆุงุจ ุจุชุทู„ุน point 993 Sigma ุดูˆ ุชุณุงูˆูŠุŸ ุฃุฑุจุนุฉ ุฃู‚ู„
265
00:22:18,950 --> 00:22:24,830
ู…ู† Z ุฃู‚ู„ ู…ู† 27 ู†ู‚ุต ู…ู† 16 ู‡ุฐูˆู„
266
00:22:24,830 --> 00:22:33,930
ุณุงู„ุจ ุชู„ุชุฉ ู…ุด ู‡ูŠูƒุŸ ู…ุงุดูŠ ุนู„ู‰ ุฃุฑุจุนุฉ ูˆ ุงู„ู„ูŠ ู‡ู†ุงุŸ
267
00:22:33,930 --> 00:22:40,210
ุจูŠู† ุงู„ุณุงู„ุจ ุชู„ุชุฉ ูˆ ุงู„ู…ูˆุฌูˆุฏ ุชู„ุชุฉ ุฌุฏุงุดุŸู„ูˆ ุงู†ุช ุนู…ู„ุชูŠู‡ุง
268
00:22:40,210 --> 00:22:43,890
ู‡ูŠุทู„ุน point nine nine seven three ุจุณ ู…ุด ู‡ุฐุง
269
00:22:43,890 --> 00:22:48,950
ุงู„ู…ุทู„ูˆุจ ุงู„ู…ุทู„ูˆุจ ูŠุชูƒู„ู… ุนู„ู‰ ู…ูŠู†ุŸ ุนู„ู‰ ุงู„ population
270
00:22:48,950 --> 00:22:52,910
ู…ูŠู†ุŸ ุนู„ู‰ ุงู„ X bar ุนู„ู‰ ุงู„ ู…ูŠูˆู…ุฉ ุนู„ู‰ ุงู„ X bar ุชุชุณุงู…ู„
271
00:22:52,910 --> 00:22:58,790
ู…ูŠู†ุŸ ุจุงู„ุชุงู„ูŠ ุฌูˆุงุจ ุฎุทุฃ ุฎุทุฃ ู„ูŠุดุŸ ู„ุฃู† ุงู„ุญู„ ู‡ู†ุง ู„ู„ X
272
00:22:58,790 --> 00:23:04,870
value ูููŠ ูุฑู‚ ุจูŠู† ุญูƒูŠ ุงู„ X ูˆ X bar ุฅุฐุง ุงู„ answer
273
00:23:04,870 --> 00:23:10,580
is B ุทุจ ุนุดุฑุฉู‚ุฑุงุกุฉ ุนู„ู‰ ุงู„ุชุงู†ูŠุฉ ุฃุฎุฑ ูˆุงุญุฏุฉ
274
00:23:31,610 --> 00:23:39,610
ุทุฑู‚ ู†ูุณ ุงู„ู…ุซู„ุฉ ู†ูุณ ุงู„ู…ุซู„ุฉ ูˆุจูŠุญูƒูŠ
275
00:23:39,610 --> 00:23:47,970
there is approximately 68 random samples of 16
276
00:23:47,970 --> 00:23:52,540
cars ู„ุญุธุฉ ุงู„ู…ุซู„ุฉ ู…ุด ุญูƒุงูŠุฉุนู†ุฏู…ุง ุดุฑูŠุช ูƒุชุงุจ ู…ูŠู† ูƒุชุงุจ
277
00:23:52,540 --> 00:23:57,580
ุจุณุงู… ุจุงู„ู…ูŠู† ูˆ ุจุณุงู… ุจุงู„ู…ูŠู†ุŸ ุชุญุช ุงู„ X bar ุชุญุช ุงู„ X
278
00:23:57,580 --> 00:23:59,440
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
279
00:23:59,440 --> 00:23:59,740
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
280
00:23:59,740 --> 00:24:01,040
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
281
00:24:01,040 --> 00:24:03,280
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
282
00:24:03,280 --> 00:24:06,400
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
283
00:24:06,400 --> 00:24:06,420
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
284
00:24:06,420 --> 00:24:08,300
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X
285
00:24:08,300 --> 00:24:11,280
barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃู‡ ุชุญุช ุงู„ X barุŸ ุฃ
286
00:24:19,720 --> 00:24:23,460
ุจุนุฏูŠู† ุจูŠุญูƒูŠ ุน ุงู„ six eight ุงู„ู„ูŠ ู‡ูŠ ุงู„ standard
287
00:24:23,460 --> 00:24:30,360
deviation ูˆุงุญุฏ ู…ุด ู‡ูŠูƒ ุงุญู†ุง ู‚ู„ู†ุง ุงู„ six eight nine
288
00:24:30,360 --> 00:24:35,320
five nine one seven ู‡ุฐุง one sigma ู‡ู†ุง two sigma ูˆ
289
00:24:35,320 --> 00:24:39,580
ู‡ุฐุง three sigma between
290
00:24:39,580 --> 00:24:43,620
ุงุฑุจุนุฉ ุนุดุฑ ูˆ ุณุช ุนุดุฑ ุงู„ sample mean ุงุฑุจุนุฉ ุนุดุฑ ู„ุบุงูŠุฉ
291
00:24:43,620 --> 00:24:50,390
ุณุช ุนุดุฑ ุงูŠุด ุฑุฃูŠูƒูˆุง ููŠ ุงู„ู…ุซู„ ู‡ุฐุงุŸู…ุงุฐุง ุฑุฃูŠูƒ ูŠุง ุณู„ุงู…ุŸ
292
00:24:50,390 --> 00:24:55,230
random sum ูŠุจู‚ู‰ ูƒู… ูƒุงุฑ ุนู†ุฏู‡ุŸ 16 ุฅุฐุง ุงู„ุฃู† ุจูŠุณุงูˆูŠ 16
293
00:24:55,230 --> 00:25:00,030
ู…ุด ู‡ูŠูƒ ุฅุฐุง ุฅุนุทุงู†ูŠ ุงู„ุฃู† ุงู„ุชุงุณุน ุจู‚ุฏุฑ ุงู†ุง ุฃุญุณุจ ู…ูŠู†ุŸ
294
00:25:00,030 --> 00:25:10,070
ุณูŠุฌู…ุง X bar ุฅูŠุด ุจุชุณุงูˆูŠุŸ ุงู„ุณูŠุฌู…ุง ู‚ุฏุงุดุŸ ุนู„ู‰ 16 ุทู„ุน
295
00:25:10,070 --> 00:25:15,260
ุณูŠุฌู…ุง X bar ุจู‚ู‰ 4 ุนู„ู‰ 16 square root ุจุทู„ุน ุจ1ุฃูˆ ุฒูŠ
296
00:25:15,260 --> 00:25:18,960
ู…ุง ุญูƒูŠุช ู„ูƒ ู…ุธุจูˆุท ุฅุฐุง ุงู„ุญุงู„ ุชุจู‚ู‰ ู‡ุงูŠู… ุจุณ ุจูŠูƒูˆู† ูˆู†
297
00:25:18,960 --> 00:25:22,440
ุงุณุชู†ุธู ูŠุงุดูŠ ุฅุฐุง ุงู„ู€ mu minus one sigma x bar
298
00:25:22,440 --> 00:25:27,300
ุจุชูƒู„ู…ู‡ุง ุงู„ x bar ู…ุด ู‡ูŠ ู…ุฑุฉ ุชุงู†ูŠุฉ there is
299
00:25:27,300 --> 00:25:31,180
approximately 68 chance that random sample of 16
300
00:25:31,180 --> 00:25:34,540
cars will have mean sample mean ุฃู†ุชูŠุด ุญู„ู‡ุง
301
00:25:34,540 --> 00:25:39,180
ุจุงู„ุทุฑูŠู‚ุฉ ุงู„ุนุงุฏูŠุฉ ุจุฏูŠ ุฃุญู„ู‡ุง ุจุงู„ empirical ruleุฅุฐุง
302
00:25:39,180 --> 00:25:43,300
ู…ูŠูˆ minus X bar ูˆ ู…ูŠูˆ plus ู…ูŠู†ุŸ Sigma X barุŒ
303
00:25:43,300 --> 00:25:51,080
ู…ุธุจูˆุทุŸ ู„ู…ูŠูˆ ู‚ุฏุงุดุŸ ุฎู…ุณุฉ ุนุงุดุŸ ูˆุงุญุฏ Sigma X bar ุจูˆุงุญุฏ
304
00:25:51,080 --> 00:25:58,400
ูˆุงู„ุชุงู†ูŠุฉุŸ ุฎู…ุณุฉ ุนุงุดุŸ ุฅูŠุด ุงู„ุฌูˆุงุจ ุจุทู„ู‚ุŸ ุฅุฐุง ูƒู„ุงู…ู‡
305
00:25:58,400 --> 00:26:03,300
ู…ุงู„ู‡ุŸ ูƒู„ุงู… ุตุญ ู„ูˆ ู…ุงุดุชุบู„ุชูŠุด ุนู„ู‰ ุงู„ rule ุงู„ู„ูŠ ุฃู†ุง
306
00:26:03,300 --> 00:26:08,750
ุญูƒูŠุชู‡ ุจุชุญู„ูŠ ุนุงุฏูŠ ูƒูŠู ุฃุญู„ูŠ ุนุงุฏูŠุŸ ุฒูŠ ุงู„ุทุฑูŠู‚ุฉ ู‡ุฐู‡ุฅูŠุด
307
00:26:08,750 --> 00:26:14,870
ู‡ุตูŠุฑ ุงู„ู…ุซุงู„ุฉุŸ ู„ูˆ ุจุฏุฃ ุฃุญู„ ุงู„ุทุฑูŠู‚ุฉ ุงู„ุนุงุฏูŠุฉ ุชุดูˆู ุฃู†ุช
308
00:26:14,870 --> 00:26:20,510
ุบุงู„ุจุง ู…ุด ู‡ุชุชุฐูƒุฑ ุงู„ empirical roleุŒ ู…ุธุจูˆุทุŸ ู‡ุจุฏุฃ ุฃุญู„
309
00:26:20,510 --> 00:26:24,490
ุจุงู„ุทุฑูŠู‚ุฉ ุงู„ุนุงุฏูŠุฉ ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุด ุงู„ probability
310
00:26:24,490 --> 00:26:28,350
between
311
00:26:28,350 --> 00:26:34,470
14 ูˆ 16 ู„ู„ expertุŒ ู…ุธุจูˆุทุŸ ุจุฏุฃ ุฃุดูˆู ุงู„ุฌูˆุงุจ ู‡ูˆ
312
00:26:34,470 --> 00:26:39,680
ุฃุนุทุงู†ูŠ yeah0.6826 ู…ุด ู‡ูŠูƒ ุจูŠุชุฃูƒุฏ ู…ู† ุงู„ุฅุฌุงุจุฉ ุงู„ู„ูŠ
313
00:26:39,680 --> 00:26:46,160
ู‡ู†ุง ุฅูŠุด ุชุนู…ู„ู‡ุง ุชุญูˆู„ูŠู‡ุง ู„ุฒูŠ ุฅูŠุด ุจุชุตูŠุฑ ู‡ูŠ 14 ู†ู‚ุต 15
314
00:26:46,160 --> 00:26:52,560
Sigma X bar ุฃู†ุง already ุญุณุจุชู‡ุง ูˆุงุญุฏ ุฃู‚ู„ ู…ู† Z ุฃู‚ู„
315
00:26:52,560 --> 00:26:57,000
ู…ู† 16 minus 15 ุนู„ู‰ 1 ู…ุด ู‡ูŠูƒ ู…ุด ู‡ูŠูƒ ู‡ุชุณุงูˆูŠ negative
316
00:26:57,000 --> 00:27:02,090
oneู„ุฃู† ูˆุตู„ุช ู„ู„ Z between minus one and plus one ู„ูˆ
317
00:27:02,090 --> 00:27:05,990
ุฑุฌุนุช ุฅู„ู‰ ุงู„ empirical rule ู„ูˆ .. ู…ู† ุบูŠุฑ .. ู…ู† ุบูŠุฑ
318
00:27:05,990 --> 00:27:08,050
ุงู„ table .. ุฃู†ุง ุจุชุญูƒูŠ ู…ู† ุบูŠุฑ ุงู„ table ู„ูˆ ุฑุฌุนุช ุฅู„ู‰
319
00:27:08,050 --> 00:27:11,970
ุงู„ empirical rule ูƒุงู† ูŠุญูƒูŠ 68% of the data will
320
00:27:11,970 --> 00:27:16,590
fall below one standard deviation of the
321
00:27:16,590 --> 00:27:21,550
population mean ู…ู‡ูŠู‡ุง .. ู…ู‡ูŠู‡ุง ุงู„ Z ุจุงู„ุณู„ุจ one and
322
00:27:21,550 --> 00:27:27,250
plus one ู‡ุฐู‡ ุงู„ area 68.23% ู…ู† ุบูŠุฑ ุงู„ tableู„ูˆ ุจุฏู‰
323
00:27:27,250 --> 00:27:31,550
ุงุณุชุฎุฏู… ุงู„ table ู‡ุฐูŠ ู…ุด ู‡ุชุณุงูˆูŠ z less than one
324
00:27:31,550 --> 00:27:36,710
ู…ุธุจูˆุท minus z less than negative one ู„ูˆ ุชุทู„ุน ุนู„ู‰
325
00:27:36,710 --> 00:27:41,970
ุงู„ table ุนู†ุฏ ุงู„ูˆุงุญุฏ ุนู†ุฏ ุงู„ูˆุงุญุฏ ุชู…ุงู†ูŠุฉ ุฃุฑุจุนุฉ ูˆุงุญุฏุฉ
326
00:27:41,970 --> 00:27:49,390
ุชู„ุงุชุฉ minus minus ุดูˆููˆุง ูุนู„ุง less than one ู„ูŠู„ูŠ
327
00:27:49,390 --> 00:27:53,070
ู‡ุฐู‡ ูƒู„ู‡ุง less than negative one ูˆุงุญุฏ minus ู‡ุฐู‡
328
00:27:53,990 --> 00:27:56,850
ู…ุธุจูˆุทุŸ ุงู„ู„ูŠ ู‡ูˆ ู„ูˆ ุทู„ุนุช ุงู„ table ุชู„ุนุจ point one
329
00:27:56,850 --> 00:28:00,410
five eight seven ู…ุด ู‡ูŠูƒ ุงูˆ ู„ูˆ ุทู„ุนุช ุนู„ู‰ ุงู„ negative
330
00:28:00,410 --> 00:28:04,510
table ู‡ุงุฎุฏู‡ ู†ูุณ ุงู„ุงุฌุงุจุฉ ู„ูˆ ุทู„ุนุช ุงู„ูุฑู‚ ู…ุง ุจูŠู† ู‡ุฏูˆู„
331
00:28:04,510 --> 00:28:10,170
ู…ุคูƒุฏ ุงู„ุฌูˆุงุจ ุงู„ู„ูŠ ู‡ูˆ ูƒูŠูƒูˆ point six twenty six
332
00:28:10,170 --> 00:28:18,110
ุทุฑูŠู‚ุฉ ู…ูŠู† ู„ุณู‡ ุทุจ ุฃุนู…ู„ ูƒู„ ุงู„ุดุบู„ ู‡ุฐุง ูˆ ุนู„ุดุงู† ุงู„
333
00:28:18,110 --> 00:28:22,890
empirical law ุงู„ empirical law ุงู„ูˆุงุถุญ ุดูˆู ุงูŠู‡ุงู„ู€
334
00:28:22,890 --> 00:28:28,390
Probabilities ุฃู†ุง ุญุงูุธู‡ู… 68959917
335
00:28:28,390 --> 00:28:33,090
ุงุดุชุบู„ ุนู„ูŠู‡ุง ุจุณ ุจุชูƒูˆู† ู…ุฑูƒุฒ ู‡ู„ ู‡ูŠ ู„ู„ X ูˆู„ุง ู„ู„ X bar
336
00:28:33,090 --> 00:28:37,590
ุงู„ู‚ุงู†ูˆู† ู…ุงุชุบูŠุฑุด ุงู„ู‚ุงู†ูˆู† ุงุดูƒุงู„ ุนุจุงุฑุฉ ุนู† ู…ูŠู† ุงู„ู€ Mu
337
00:28:37,590 --> 00:28:43,210
minus Sigma ู…ุธุจูˆุท ุงู„ู€ Mu plus Sigma ู…ุด ู‡ูŠูƒุŸ ุงุฐุง ู‡ูŠ
338
00:28:43,210 --> 00:28:45,630
ู„ู„ X ูŠุนู†ูŠ ุงู„ values ู†ูุณู‡ุง ุจุชูƒูˆู† ู…ูŠู† ู„ู„ X ูˆ Sigma
339
00:28:45,630 --> 00:28:50,370
ู„ู„ X ู…ุด ู‡ูŠูƒุŸ ูˆู‡ุฐุง ู…ุชุณุงูˆู‰ ูƒุฏู‡ ูŠุง ุนุดุงู† 68
340
00:28:53,040 --> 00:28:57,540
ุทุจ ู„ูˆ ุญุงุฌุฉ ุฒูŠ ู‡ูŠูƒ ุงู„ sample mean ุจุตูŠ ู†ูุณู‡ุง ุจุงู„ุธุจุท
341
00:28:57,540 --> 00:29:06,280
ุจุณ ุงุฎุชู„ุงู ู‡ูŠุด ูƒู„ ุญู…ู„ุฉ just replace this x by x bar
342
00:29:06,280 --> 00:29:13,480
ุจุณ ู‡ูŠ ุงู„ู„ูŠ ุจุนู…ู„ู‡ ูˆ ู†ูุณ ุงู„ู†ุณุจุฉ ุจุงู„ุชุฃูƒูŠุฏ ุจุณ ุนู†ุฏูŠ
343
00:29:13,480 --> 00:29:17,340
ู…ุดูƒู„ุฉ ูˆุงุญุฏุฉ ุงู†ู‡ ู„ุงุฒู… ุงุญุณุจ mean sigma x barุนุดุงู†
344
00:29:17,340 --> 00:29:21,420
ุฃุญุณุจู‡ุง ุงู„ู‚ุงู†ูˆู† sigma over square root of n ู„ูˆ ุงู„ุฃู†
345
00:29:21,420 --> 00:29:25,820
ู…ุด ู…ุนู„ูˆู…ุฉ ู…ู‚ุฏุฑุด ุฃูƒู…ู„ ุนุดุงู† ุฐู„ูƒ ุงู„ู…ุซู„ ุงู„ู„ูŠ ูุงุช
346
00:29:25,820 --> 00:29:30,980
ู…ูƒู…ู„ุชุด ู„ุฃู†ู‡ ุงู„ุฃู† ู…ุงูƒุงู†ุชุด ู…ูˆุฌูˆุฏุฉ ูˆุงุถุญุŸ ูˆุงุถุญ ููŠ ุฃูŠ
347
00:29:30,980 --> 00:29:38,440
ุณุคุงู„ุŸ ุฎู„ุงุต ุฃูŠู‡ ุนุดุฑ ุงู„ุณู„ุฉุŸ ูˆุงุถุญ
348
00:29:38,440 --> 00:29:41,620
ูƒุฏู‡ ุจููƒุฑ ููŠ ุญุงู„ ู…ุซู„ู‡ุงุŸ ู†ุนู… ุฏู‡ ูŠูƒูˆู† ุบุงุถุจ ุงู„ู…ุจุฏุฃ
349
00:29:41,620 --> 00:29:46,150
ูƒูˆูŠุณ ูู‡ู…ู‡ ูƒูˆูŠุณ ูˆุงู„ู…ุจุฏุฃ ููŠ ุงู„ุญู„ุฎู„ุงุต .. ุฎู„ุงุต ุงู„
350
00:29:46,150 --> 00:29:49,910
chapter 7 ูˆุงู„ู„ู‡
351
00:29:49,910 --> 00:29:56,470
ู…ุด ุนุงุฑู ุทู„ุน ุนู„ูŠู‡ู… ุจุฏูƒ
352
00:29:56,470 --> 00:30:04,470
11 ูˆ 12ุŒ ู‡ุงูŠ 11 ูˆ 12 ุจุฑุถู‡
353
00:30:04,470 --> 00:30:09,290
ุฎู„ูŠู†ุง ู†ูƒู…ู„ ู†ูุณ ุงู„ scenario ุงู„ู„ูŠ ูุงุชุญ ุงู„ time spent
354
00:30:09,290 --> 00:30:14,660
studying by students in the weekfor the final exam
355
00:30:14,660 --> 00:30:16,540
follows normal distribution with standard
356
00:30:16,540 --> 00:30:23,760
deviation of 8 ุงุฐุง sigma 8 a random sample of 4
357
00:30:23,760 --> 00:30:33,720
students ุงู„ N is 4 ูˆุนู†ุฏูŠ ุชูˆุฒูŠุน ุทุจูŠุนูŠ ู…ุด ูƒุฏู‡ was
358
00:30:33,720 --> 00:30:36,920
taken in order to estimate the mean study time for
359
00:30:36,920 --> 00:30:42,600
the population of all studentsูŠุนู†ูŠ ุงุฎุฏ random
360
00:30:42,600 --> 00:30:45,220
sample ุจุงุฑุจุนุฉ ูˆ ุงู„ุงุฑุจุนุฉ ู‡ุฏูˆุฉ ุจูŠุนู…ู„ estimation
361
00:30:45,220 --> 00:30:50,040
ู„ู…ูŠู†ุŸ ู„ู„ู…ูŠู† ุงู„ุตุงุฏุฑ ู„ูƒู„ ุงู„ population ุจุญูƒูŠ what's
362
00:30:50,040 --> 00:30:55,480
the probability that the sample mean ุงูŠุด ุงุญุชู…ุงู„ ุงู†
363
00:30:55,480 --> 00:30:58,900
ุงู„ sample mean ู…ุง ู„ูˆ exceed the population mean
364
00:30:58,900 --> 00:31:05,860
ุจุฒูŠุฏ ุนู† ุงู„ population meanุฃูƒุจุฑ ู…ู† ุงู„ population
365
00:31:05,860 --> 00:31:10,520
mean by more than two hours ู‡ู„ุฃ ู†ูƒุชุจ ู‡ูŠูƒ exceed
366
00:31:10,520 --> 00:31:16,340
ูŠุนู†ูŠุด ุฃูƒุจุฑ ู…ู† ู…ูŠู†ุŸ ู…ู† ุงู„ mean ู…ู† ุงู„ mean ุจุฌุฏุงุดุŸ
367
00:31:16,340 --> 00:31:19,820
population ุจุงุชู†ูŠู† ุจุงุชู†ูŠู† ุจุณ ุงุชู†ูŠู† x bar ู†ู‚ุต ู…ูŠูˆ
368
00:31:19,820 --> 00:31:25,580
ุฃูƒุจุฑ x bar ุฃูƒุจุฑ ู…ู† ู…ูŠูˆ plus ุงุชู†ูŠู† ู…ุด ู‡ูŠูƒ ู‡ูˆ ู…ุด
369
00:31:25,580 --> 00:31:29,140
ุจูŠุญูƒูŠ ุงู„ sample mean exceed the population mean by
370
00:31:29,140 --> 00:31:32,600
more than two hours ุงู‡ ูŠุนู†ูŠ ู‡ูˆ ู…ุถุนู ุนู„ู‰ ุงุชู†ูŠู† ู‡ูˆ
371
00:31:32,600 --> 00:31:39,980
ู…ุถุนู ุนู„ู‰ ุงุชู†ูŠู†ู…ุด ุงู„ู…ุดูƒู„ุฉ ุงูุถู„ ู„ุฃ ุงูˆ ูƒุงู…ู„ ูŠุนู†ูŠ ู‡ูˆ
372
00:31:39,980 --> 00:31:45,360
ุจุฏู‡ .. ุจุฏู‡ ุงู„ุฌูˆุงุจ ุงู„ู„ูŠ ู‡ู†ุง ู…ุธุจูˆุท
373
00:31:45,360 --> 00:31:49,860
ุงูƒู…ู„ ุงู„ุญู„ู‚ุฉ ุงู‡ ู…ุธุจูˆุท ูŠุนู†ูŠ ุงู„ ู…ูŠูˆ ุจุชุฑูˆุญ ู…ุน ุงู„ู…ูŠูˆ
374
00:31:49,860 --> 00:31:58,660
ุญุงูˆู„ ู„ุฒูŠ score ูƒูŠู ุฒูŠ ูŠุตูŠุฑ ุงู„ score ุจูŠุตูŠุฑ
375
00:31:58,660 --> 00:32:03,450
ุงู„ x bar minus ู…ูŠูˆSigma over square root of n
376
00:32:03,450 --> 00:32:08,930
ู…ุธุจูˆุท ุฃูƒุจุฑ ู…ู† ู„ุฃ ุฒูŠ ู…ูŠูˆ ุจู„ุณ ุงู„ุชูŠู† ู…ูˆุฌูˆุฏุฉ minus ุงู„
377
00:32:08,930 --> 00:32:12,050
ู…ูŠูˆ minus ุงู„ ู…ูŠูˆ ุจูŠุฑุญู„ ู…ุน ุจุนุถ ุนู„ู‰ ุณูŠุฌู…ุง ุนู„ู‰ square
378
00:32:12,050 --> 00:32:15,930
root of n ูƒู…ุด ุงู„ุณูŠุฌู…ุง ุชู…ุงู†ูŠุฉ ุนู„ู‰ ุงุชู†ูŠู† ุงูˆ ุฌุฒุก ู…ู†
379
00:32:15,930 --> 00:32:20,350
ุงู„ุฃุนู„ู‰ ูŠุนู†ูŠ ุฏู‡ ู‡ุชุณุงูˆูŠ ุจ ุฃุฏ ุฒูŠ ู…ุด ู…ุธุจูˆุท ุฒูŠ ุงู‡ ุงู‡
380
00:32:20,350 --> 00:32:25,210
ุงู„ู…ูŠูˆ ุฑุงุญุช ุงุชู†ูŠู† ุชู…ุงู†ูŠุฉ ุนู„ู‰ ุงุชู†ูŠู† ุงุฑุจุนุฉ ุงุชู†ูŠู† ุนู„ู‰
381
00:32:25,210 --> 00:32:29,790
ุงุฑุจุนุฉ ู†ุต ุจุชุทู„ุน ูƒู„ู‡ ู†ุต ูŠุนู†ูŠ ุนุงูŠุฒ ูŠุจู‚ู‰ ุจู„ุชูˆู ุฒูŠ
382
00:32:29,790 --> 00:32:37,660
greater than point Fุจู†ุทู„ุญู‡ุง ุนู†ุฏ 2 ุนู†ุฏ ุงู„ู†ุต one
383
00:32:37,660 --> 00:32:42,900
minus ุฅู„ู‰
384
00:32:42,900 --> 00:32:48,060
ุนู†ุฏ ุงู„ point five ุงุชุทู„ุน ุชุชุงุจุน point six nine one
385
00:32:48,060 --> 00:32:53,840
five ุจุธุจุทุŸ ุฅุฐุง ุฃุฑุดุฏ ุฌูˆุงุจ point three zero eight
386
00:32:53,840 --> 00:33:00,680
five point ุฎู„ุงุต ูุงู„ุฌูˆุงุจ ู„ูˆ ุงุชุทู„ุนุช check the answer
387
00:33:02,020 --> 00:33:07,960
ู…ุธุจูˆุท ุงู„ุฌูˆุงุจ ู‡ูŠุŸ ุงู‡ ู…ุธุจูˆุท ุทุจ ุงู„ุญู…ุฏ ู„ู„ู‡ ูŠุนู†ูŠ ู…ุนู†ู‰
388
00:33:07,960 --> 00:33:14,040
ุงู„ุณุคุงู„ ู‡ุฐุง ู…ุนู†ู‰ ุทูˆู„ ุงู„ู…ุนู†ู‰ ุงู„ููƒุฑุฉ
389
00:33:14,040 --> 00:33:20,380
ุชุงุนุชู‡ ูƒุงู†ุช ุชุงู„ูŠุฉ ุงู„ููƒุฑุฉ ู‡ูŠ find the probability
390
00:33:20,380 --> 00:33:25,500
that the sample mean exceeds ุจุฒูŠุฏ ุนู† ุงู„ population
391
00:33:25,500 --> 00:33:31,050
mean ุงู„ู„ูŠ ู‡ูˆ ุงู„ mu ุจุฒูŠุฏby 2 ู„ูˆ ุญูƒู‰ ุจู‚ู„ ูŠุนู†ูŠ ุฃู‚ู„ ู…ู†
392
00:33:31,050 --> 00:33:43,310
U plus 2 ู„ูˆ ุฃู‚ู„ ุฎู„ุงุต ุฃู‚ู„ ู…ู†ู‡ ุฎู„ุงุต ุฃูŠู‡ 22ุŸ 23ุŸ
393
00:33:43,310 --> 00:33:49,370
23 ุฃูŠู‡ 23ุŸ
394
00:33:49,370 --> 00:33:52,530
ุจุฑุถู‡
395
00:33:52,530 --> 00:33:58,210
ุงู„ sample meanis more than three hours below the
396
00:33:58,210 --> 00:34:02,850
population means ุฃูƒุชุจ
397
00:34:02,850 --> 00:34:07,950
ุจุญูŠูƒ ูˆู„ุง ุจูŠู‚ูˆู„ minus ู†ู‚ุฑุง ูƒูˆูŠุณ is more ู‡ูŠ more
398
00:34:07,950 --> 00:34:14,910
than three hours below ู‡ูŠูƒ ูˆู„ุง ู‡ูŠูƒ
399
00:34:14,910 --> 00:34:19,550
ู‡ูˆ
400
00:34:19,550 --> 00:34:26,410
ุจุญูƒู‰ is more ู‡ูŠ more ู…ุธู„ูˆู…more ู‚ุฏุงุดุŸ three hours
401
00:34:26,410 --> 00:34:30,490
below ูŠุนู†ูŠ ู‡ูˆ ุฃู‚ู„ ู…ู† ุงู„ mean ุจุชุงู†ูŠุฉ ุงู„ุณุงุนุฉ ูŠุนู†ูŠ
402
00:34:30,490 --> 00:34:36,470
ุงู„ุชุงู†ูŠุฉ ูŠุนู†ูŠ ุงู„ุชุงู†ูŠุฉ ุงู„ุตุญ ุจุงู„ุชุฑุฌู…ุฉ ู…ุด ุญุฑููŠุฉ ูˆ ุชูƒุชุจ
403
00:34:36,470 --> 00:34:41,030
more than three below three minus ู„ุฃ ู‡ูˆ ุจู‚ู„ ุนู„ู‰ ุงู„
404
00:34:41,030 --> 00:34:45,810
mean ุงู„ุชู„ุงุชุฉ ูŠุนู†ูŠ ุงู„ mean ู†ุงู‚ุต ุชู„ุงุชุฉ ูˆุงุถุญุŸ ุฅุฐุง ู‡ุฐู‡
405
00:34:45,810 --> 00:34:50,890
ู‡ูŠ ุฃูƒู…ู„ู‡ุง ู…ุด ุตุญูŠ ู‡ุชุจู‚ู‰ ุฃูƒู…ู„ุŸ ุฅุฐุง ุจุญูƒูŠ ู„ู‡ู… ุดูˆูŠุฉุŒ
406
00:34:50,890 --> 00:34:56,530
ู‡ูŠูƒุŸ- mu over sigma over root n ุญูƒูŠู†ุง sigma over
407
00:34:56,530 --> 00:35:00,590
root n ู‚ุฏูŠุด ุทู„ุนู†ุงู‡ุง ู‡ู†ุง ุชู…ุงู†ูŠุฉ ุฃุชู†ูŠู† ุฃุจู‚ู‰ ุฃุฑุจุนุฉ
408
00:35:00,590 --> 00:35:08,210
ุจุงู„ุณูˆุงุก ุจูŠ ูˆ ููŠ ุฒูŠ ุฃูƒุจุฑ ู…ู† negative ุชู„ุงุชุฉ ุนู„ู‰
409
00:35:08,210 --> 00:35:12,830
ุฃุฑุจุนุฉ ูŠุนู†ูŠ negative point seven five ู…ุธุจูˆุท ู‡ูŠ ูŠุนู†ูŠ
410
00:35:12,830 --> 00:35:17,310
ูˆุงุญุฏ minus ุฒูŠ less than negative point seven five
411
00:35:17,310 --> 00:35:19,830
ุงู„ุงู† seven five
412
00:35:22,540 --> 00:35:30,120
-0.75 2266
413
00:35:30,120 --> 00:35:36,640
ูˆูŠู†
414
00:35:36,640 --> 00:35:49,220
ุฑุงุญุช ุงู„ุฌูˆุงุจ ู†ุงู‚ุต 7.5 under 5 ู…ุด ู‡ูŠูƒ ุงู„ุฌูˆุงุจ
415
00:35:49,220 --> 00:35:51,000
2.266
416
00:35:56,910 --> 00:36:04,350
ู‡ุฐุง ุงู„ุฌูˆุงุจู„ ููŠ ุงู„ูƒุชุงุจ ู…ุด one minus ุทุจ ุฅูŠุด ุงู„ุณุจุจุŸ
417
00:36:04,350 --> 00:36:08,010
ุงู„ุฌูˆุงุจู„ ููŠ ุงู„ูƒุชุงุจ point two two six six ูŠุนู†ูŠ ุทุจุนุง
418
00:36:08,010 --> 00:36:17,910
one minus ูˆุญูƒู‰ list ุฏู‡ุŸ is more than ูˆ ุฃู†ุง ุจุชุนู…ู„ู‡ุง
419
00:36:17,910 --> 00:36:22,820
ูƒูŠู ุฒูŠ ู…ุง ุฃู†ุง ุนุงูŠุฒูŠุนู†ูŠ ุงูŠุด ุงู„ุบู„ุท ููŠ ุงู„ุญู„ุŸ ุงู‡ ู„ุญุธุฉ
420
00:36:22,820 --> 00:36:28,460
ุดูˆูŠุฉ ู‡ุงูŠ ุงู„ scenario ุงู„ุฃูˆู„ ู…ุดูŠู‡ุงุŸ ุทุจ
421
00:36:28,460 --> 00:36:35,160
ุงุฐุง ุนู…ู„ุช P of X bar ุฃูƒุจุฑ ู…ู† ุชู„ุงุชุฉ ู†ู‚ุต ู…ูŠูˆ ุฅูŠุด
422
00:36:35,160 --> 00:36:44,780
ู‡ุชุตูŠุฑุŸ ุชู„ุงุชุฉ ู†ู‚ุต ู…ูŠูˆ ู†ู‚ุต ู…ูŠูˆ ูˆ ุงู„ sigma ุนู„ู‰ .. ุงู„
423
00:36:44,780 --> 00:36:49,310
sigma ุงู„ ุชู…ุงู†ูŠุฉ ุนู„ู‰ ุงุชู†ูŠู† ุจุงุฑุจุนplus ู‡ุฐู‡ ูˆ ุจุนุฏูŠู†
424
00:36:49,310 --> 00:36:53,090
ู‡ุฐู‡ ุตุงุฑุช ุณุงู„ุจ ุงุชู†ูŠู† ู…ูŠูˆ ุณุงู„ุจ ุงุชู†ูŠู† ู…ูŠูˆุŸ ุชู„ุงุชุฉ ู†ู‚ุต
425
00:36:53,090 --> 00:36:56,670
ุงุชู†ูŠู† ู…ูŠูˆุŸ ู…ู† ุงูŠู† ุงุฌูŠุจ ุงู„ู…ูŠูˆ ุทูŠุจุŸ ุงู„ู…ูŠูˆ ู…ุด ู…ุนุฑูˆู
426
00:36:56,670 --> 00:36:59,530
ู…ุด ู…ุนุฑูˆูุŸ ู‡ุฐุง ุงู„ุทุฑูŠู‚ ุงุตู„ุง ุงุฐุง ู‡ุฐุง ู…ุณุชุญูŠู„ ุชูƒูˆู† ุตุญ
427
00:37:01,330 --> 00:37:07,870
ู‡ุฐู‡ ู‡ูŠูƒ ู…ุด ุตุญ ู„ุฃ ู‡ูŠ ุงู„ุณุคุงู„ ุงู„ุญุงู„ูŠ ุตุญ ุจุณ ุงู„ุฌูˆุงุจ ู‡ูŠู‡
428
00:37:07,870 --> 00:37:11,710
ุงู†ุง ุงุดุชุบู„ู‡ุง ู…ุนุงู‡ ู…ูŠูˆ ู†ู‚ุตุฉ plus negative three
429
00:37:11,710 --> 00:37:16,490
ู…ุธุจูˆุท ู‡ู†ุง ุนู„ู‰ negative point seven five ุฃูƒุจุฑ ู…ู†ู‡ุง
430
00:37:16,490 --> 00:37:22,810
ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุงู„ negative ู…ุธุจูˆุท ู‡ุฐุง ุฃูƒุจุฑ ู…ู† ุงู„ุฃูƒุจุฑ
431
00:37:22,810 --> 00:37:26,890
ู…ู† ู‡ูŠ ุงู„ุฃูƒุจุฑ
432
00:37:26,890 --> 00:37:31,360
ู…ู† negative ุฃูƒูŠุฏ ุฃูƒุชุฑ ู…ู† ู†ุต ุงู„ุฌูˆุงุจุงู„ุฌูˆุงุจ ู‡ูˆ point
433
00:37:31,360 --> 00:37:35,380
seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven
434
00:37:35,380 --> 00:37:35,380
three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four
435
00:37:35,380 --> 00:37:35,560
ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ
436
00:37:35,560 --> 00:37:36,480
point seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven
437
00:37:36,480 --> 00:37:39,300
seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three
438
00:37:39,300 --> 00:37:41,160
four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ
439
00:37:41,160 --> 00:37:41,460
ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point
440
00:37:41,460 --> 00:37:41,540
seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven
441
00:37:41,540 --> 00:37:41,540
three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four
442
00:37:41,540 --> 00:37:41,540
ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ
443
00:37:41,540 --> 00:37:41,540
point seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven
444
00:37:41,540 --> 00:37:41,540
seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three
445
00:37:41,540 --> 00:37:41,540
four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ
446
00:37:41,540 --> 00:37:41,540
ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point
447
00:37:41,540 --> 00:37:42,520
seven seven three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven
448
00:37:42,520 --> 00:37:43,260
three four ุงู„ุฌูˆุงุจ ู‡ูˆ point seven seven three four
449
00:37:43,260 --> 00:37:46,680
ุงู„ุฌูˆุงุจ
450
00:37:46,680 --> 00:37:49,920
ู‡ูˆ point seven seven three four ุงู„ุฌูˆุงุจ
451
00:37:59,090 --> 00:38:05,290
ุงู„ุฌูˆุงุจ ู‡ุฏู 23 ุงู„ุฌูˆุงุจ ู‡ูŠ 0.7734 ุฅุฐุง
452
00:38:05,290 --> 00:38:08,530
ุงู„ููƒุฑุฉ ูƒุงู†ุช ู‡ูˆ ุนุงูŠุฒ ุงู„ sample mean ุงู„ู„ูŠ ู‡ูˆ ุงู„ expo
453
00:38:08,530 --> 00:38:14,410
ุฃูƒุจุฑ more than three hours below the population
454
00:38:14,410 --> 00:38:18,190
ุฏูƒุชูˆุฑ ุทุจ ุจูŠูุนู„ ู…ุซู„ุง ู†ุฑุณู…ู‡ ู‡ูƒุฐุง ู†ุฑุณู… ุงู„ุฃุดูŠุงุก ูˆ ู†ุดูˆู
455
00:38:18,190 --> 00:38:23,010
ูƒุฏู‡ ู…ุง ูŠุชูˆุตู„ ู„ู†ุง ุฒูŠู‡ุง ูู„ุฃ ู‡ูˆ ุจูŠุญูƒูŠ ุฃู†ู‡ ู‡ุงูŠ ุงู„ mean
456
00:38:23,010 --> 00:38:29,740
ุงู„ expo ุงุฑู…ุงู„ู‡ุงู„ุณู…ุจู„ ูŠุนู†ูŠ ุฃูƒุจุฑ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„
457
00:38:29,740 --> 00:38:35,600
population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population
458
00:38:35,600 --> 00:38:39,540
ูŠุนู†ูŠ ุฃู‚ู„
459
00:38:39,540 --> 00:38:47,240
ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช
460
00:38:47,240 --> 00:38:48,460
ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population
461
00:38:48,460 --> 00:38:50,120
ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู†
462
00:38:50,120 --> 00:38:51,880
ุซู„ุงุซ ุณุงุนุงุช ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„
463
00:38:51,880 --> 00:38:52,700
population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population
464
00:38:52,700 --> 00:38:52,700
ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู†
465
00:38:52,700 --> 00:38:52,720
ุซู„ุงุซ ุณุงุนุงุช ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„
466
00:38:52,720 --> 00:38:52,720
population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population
467
00:38:52,720 --> 00:38:52,720
ูŠุนู†ูŠ ุฃู‚ู„ ู…ู† ุซู„ุงุซ ุณุงุนุงุช ุงู„ population ูŠุนู†ูŠ ุฃู‚ู„ ู…ู†
468
00:38:52,720 --> 00:38:55,730
ุซู„ุงุซุจุณ ุฅูŠุด ุญูƒุงูŠุฉุŸ ู„ุฅู† ู‡ูŠ ุนุงูŠุฒุฉ ุงู„ู…ู†ุทู‚ุฉ ุฏูŠ ุจุงู„ุธุจุท
469
00:38:55,730 --> 00:39:00,210
ู‡ูŠูƒ ุฃูŠ ู…ู†ุทู‚ุฉุŸ ุงู„ู„ูŠ ู‡ูŠูƒ ูˆู„ุง ุงู„ู„ูŠ ู‡ูŠูƒ ุฅุฐุง ุฎุฏุช ุนู„ูŠู‡ุง
470
00:39:00,210 --> 00:39:11,010
ุตุงุฑ ู…ุนู†ุงู‡ุงุด ุฅู† ุงู„ explore ุฃู‚ู„ ู‡ูˆ ุฅูŠุด ุณุฃู„ุŸ is more
471
00:39:11,010 --> 00:39:16,890
three hours below ูŠุนู†ูŠ ุชู„ุช .. ุชู„ุช ุณุงุนุงุช ุฃู‚ู„ ู…ู†
472
00:39:16,890 --> 00:39:21,940
ุงู„ู…ู‚ุงุตุทุจ ูƒุงู…ู„ุฉ ูƒูˆูŠุณุŸ ุฎุด ุชุดูˆู ุงู„ู…ูู‡ูˆู… ุทุจุนู‡ุง ู„ูˆ
473
00:39:21,940 --> 00:39:26,440
ู‚ุฏุงู…ุช ู„ูˆ ู‚ุฏุงู…ุช ุดูˆูŠุฉ ู„ู…ุง ุจู‚ุฏู… ู‡ู†ุง ุจุณ ู‡ู†ุง ุฏูŠ ู…ูŠูˆ ู†ู‚ุต
474
00:39:26,440 --> 00:39:32,200
ูƒุฏู‡ุดุŸ ู†ูŠู† .. ู†ูŠู† .. ูˆ ู‡ู†ุง .. ู†ู‚ุต ูˆุงุญุฏ .. ู†ู‚ุต ูˆุงุญุฏ
475
00:39:32,200 --> 00:39:35,060
ู…ุธุจูˆุท .. ุงู‡ ูˆ ุจุนุฏูŠู† ู…ูŠูˆ .. ูˆ ุจุนุฏุด ุงูŠู‡ ู†ู‚ุต ูˆุงุญุฏุŸ
476
00:39:35,060 --> 00:39:41,400
ุจุนุฏูŠู† ู…ูŠูˆ .. ุทุจ ุฃู†ุง ุนุงูŠุฒ ู‡ูŠุดุŸ ุฃูƒุชุฑ ู…ู† .. ุทุจ ุฃูƒุชุฑ
477
00:39:41,400 --> 00:39:44,680
ู…ู† ุชุนุงู„ูŠ ู†ุงุญูŠุฉ ุงู„ุชุงู†ูŠุฉุŒ ุฅูŠุด ู‡ุชุตูŠุฑุŸ ู†ู‚ุต ุฃุฑุจุนุฉ .. ูˆ
478
00:39:44,680 --> 00:39:51,190
ู‡ูƒุฐุงุŒ ุฅุฐุง ุฃู†ุง ุนุงูŠุฒ ูˆูŠู†ุŸูŠุนู†ูŠ ุนุงูŠุฒ ู‡ุงุฏ ุงู„ู…ู†ุทู‚ุฉ ูŠุนู†ูŠ
479
00:39:51,190 --> 00:39:54,510
ู…ุทู„ูˆุจ probability of x minus less than u minus
480
00:39:54,510 --> 00:39:59,490
three ุจุงู„ุฑุบู… ุฃู†ู‡ ุญูƒู‰ more ุจุณ ุนุดุงู† ุญูƒู‰ three hours
481
00:39:59,490 --> 00:40:03,910
below ูู…ุนุฑุงุณูŠ ู…ุจูŠู†ุฉ ุฅุฐุง ู…ุง ุฃูƒุฏ ุงู„ุดุบู„ ู‡ู†ุง ุตุญ ุจุณ
482
00:40:03,910 --> 00:40:08,530
ุงู„ู„ูŠ ู‡ุงุฏ ู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู†ู‡ ุฅุฐุง ู…ุง ุฃูƒุฏ ู‡ุงุฏ ุนู…ู„ู‡ุง
483
00:40:08,530 --> 00:40:14,780
replaceู„ุง ู‚ู„ู†ุง ูŠุนู†ูŠ ุงู„ุฑุณู… ูŠุง ุฏูƒุชูˆุฑ ู‡ูˆ ุงู„ู„ูŠ ุจูŠุจูŠู†
484
00:40:14,780 --> 00:40:20,620
ุทุจุนุงุŒ ุงู…ุชุงุฒุฉ ุงู„ุฑุณู… ู‡ูˆ ุงู„ู„ูŠ ุจูŠุจูŠู† ูˆู‡ูŠ ุงู„ุฌูˆุงู†ุจ ุจุญุซ
485
00:40:20,620 --> 00:40:24,140
ููƒุฑุฉ ุงู„ู…ุซู„ุฉ ุงู„ุขู† ู„ูˆ ู…ุดูŠุช ุจุงู„ุทุฑูŠู‚ุฉ ุงู„ุนุงุฏูŠุฉ ู…ู† ุบูŠุฑ
486
00:40:24,140 --> 00:40:28,400
ู…ุฑุณูˆู… more than three hours ู„ูˆ ุฌุงู„ above the mean
487
00:40:28,400 --> 00:40:33,180
ุฎู„ุงุต above the mean ูŠุนู†ูŠ ู‡ู†ุง ูƒูŠู ุชุตูŠุฑ ู„ูˆ above the
488
00:40:33,180 --> 00:40:40,470
meanุŸ ุฑูƒุฒ ู…ุนุงู‡ุŒ ู‡ูŠ ุงู„ meanู„ูˆ ุญูƒู‰ more than three
489
00:40:40,470 --> 00:40:43,310
hours above the mean ู‡ุงูŠ above the mean ู…ุธุจูˆุท ู„ูˆ
490
00:40:43,310 --> 00:40:47,530
ู‡ูŠ ู…ูŠูˆ ุจู„ุณ ุชุฑูŠ ุญูƒู‰ more than three hours ู‡ูŠุด ุญุตูŠุฑ
491
00:40:47,530 --> 00:40:50,790
ู…ูŠูˆ ุฒูŠ ุงู„ุฃุฑุจุนุฉ ู‡ู†ุง ู…ุธุจูˆุท ู„ู…ุง ูƒุฏู‡ ุงู„ู…ุณุงุญุฉ ุงู„ูŠ ุนู†
492
00:40:50,790 --> 00:40:55,570
ุงู„ูŠู…ูŠู† ู„ูƒู† ู„ู…ุง ุญูƒู‰ ู…ูŠูˆ ุงูˆ ุงู„ sample mean is more
493
00:40:55,570 --> 00:41:00,550
than three hours belowู„ู…ุง ุจู…ุดูŠ ู‡ูƒ ู…ูŠูˆ ู…ุงูŠู†ูˆุณ ุซู„ุงุซุŒ
494
00:41:00,550 --> 00:41:03,690
ุฅูŠุด ุจูŠูƒูˆู† ุนู„ู‰ ุงู„ุดู…ุงู„ุŸ ุฃุฑุจุนุฉ ุฃูˆ ุฎู…ุณุฉ ุฃูˆ ุณุชุฉ ูˆ ู‡ูƒุฐุง
495
00:41:03,690 --> 00:41:06,770
ูˆ ุนู„ู‰ ุงู„ูŠู…ูŠู† ู…ุงูŠู†ูˆุณ ุงุชู†ูŠู† ูˆ ู…ุงูŠู†ูˆุณ ูˆุงุญุฏ ูุจุงู„ุชุงู„ูŠ
496
00:41:06,770 --> 00:41:09,730
ุฃู†ุง ุนุงูŠุฒ ุฃู„ุงู‚ุฑุง ููŠู‡ุง land to the left ููŠู‡ุง ุฏูŠุŒ
497
00:41:09,730 --> 00:41:16,470
ุฎู„ุงุตุŸ ุฅุฐุง ุฃุฎุฏู‡ุง ุฏุงูŠู…ุง ุจุงู„ุนูƒุณุŒ ุฅุฐุง ุญูƒู‰ below ูˆ ุญูƒู‰
498
00:41:16,470 --> 00:41:21,290
more thanุŒ ุฅุฐุง ุญูƒูŠ more ูˆ ู‡ู†ุง belowุŒ ุฃุฎุฏู‡ุง ุฃู‚ู„ ุนู„ู‰
499
00:41:21,290 --> 00:41:26,640
ุทูˆู„ุŒ ููŠ ุงู„ู…ุซู„ ุฅูŠุด ุญูƒูŠ ุงู„ุฃูˆู„ุงู†ูŠุฉุŸ more ู‡ูŠุจุณ ุฅูŠุดุŸ
500
00:41:26,640 --> 00:41:30,960
why moreุŸ ููŠ ู†ูุณ ุงู„ direction ุจุงุฎุฏ ุฃูƒุจุฑ ุนู„ู‰ ุทูˆู„ ุจุณ
501
00:41:30,960 --> 00:41:33,880
ุชู‚ูˆู„ูˆุง ู„ูˆ ุฅุญู†ุง ุงู†ุชุจู‡ู†ุง ุฃุตู„ุง ู‡ูˆ ู‡ุงุฏูŠ more ุชุจุน ู„ุฅู†ู‡
502
00:41:33,880 --> 00:41:36,420
ุงู„ูุฑู‚ ุจูŠู† ุงู„ mu ุชุจุน ุงู„ sample ูˆ ุงู„ mu ุชุจุน ุงู„
503
00:41:36,420 --> 00:41:39,100
population ู…ุงู„ู‡ุงุด ุฏุฎู„ ุจุงู„ probability ูŠุนู†ูŠ ุจุญูƒูŠู„ูƒ
504
00:41:39,100 --> 00:41:42,200
ุฅุญุชู…ุงู„ูŠุฉ ุฅู† ุงู„ sample ู…ูŠู† ู‡ูˆ ุงู„ุฃูƒุชุฑ ู…ู† ุงู„
505
00:41:42,200 --> 00:41:46,380
population ู…ูŠู†ุŸ ุงู„ probability ู‡ูˆ ุทุงู„ุจ ุงู„
506
00:41:46,380 --> 00:41:49,240
probability ู„ู„ sample ู…ูŠู†ุŸ ุงู‡ ูŠุนู†ูŠ more ู‡ุงุฏูŠ more
507
00:41:49,240 --> 00:41:52,920
ู…ุงู„ู‡ุงุด ุฏุฎู„ ุจุงู„ probability ู„ุฃ ุฅู„ู‰ ุฏุงุฎู„ ูˆูŠู†ุŸ ุฅู†ู‡
508
00:41:52,920 --> 00:41:57,360
ุฃู†ุง ุนุงูŠุฒ ุงู„ sample ู…ูŠู†ุŸูŠูƒูˆู† ุฃูƒุชุฑ ู…ู† ุงู„ population
509
00:41:57,360 --> 00:42:03,640
mean ุจ 3 ุณุงุนุงุช ุจุณ below ูŠุนู†ูŠ ู…ูŠูˆ minus 3 minus 4
510
00:42:03,640 --> 00:42:06,140
minus 5 and so on