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1
00:00:20,670 --> 00:00:22,250
ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู…

2
00:00:22,250 --> 00:00:24,090
ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

3
00:00:24,090 --> 00:00:24,410
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

4
00:00:24,410 --> 00:00:25,210
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

5
00:00:25,210 --> 00:00:25,590
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

6
00:00:25,590 --> 00:00:26,070
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

7
00:00:26,070 --> 00:00:26,170
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

8
00:00:26,170 --> 00:00:26,190
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

9
00:00:26,190 --> 00:00:26,190
ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡

10
00:00:26,190 --> 00:00:29,330
ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู…

11
00:00:29,330 --> 00:00:36,810
ุจุณู…

12
00:00:36,810 --> 00:00:37,810
ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู†

13
00:00:37,810 --> 00:00:43,290
ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญู…ู† ุงู„ุฑุญ

14
00:00:47,280 --> 00:00:49,700
ุฅูŠุด ุฃู†ุชูˆุง ุนุงูŠุฒูŠู†ุŸ ุงุนู†ูŠ ุงุฏูŠู†ูŠ ุณุคุงู„ ู…ุญุฏุฏ ุงูุถู„ ุงูŠู‡

15
00:00:49,700 --> 00:00:52,520
ุจู‚ู‰ ุฃูˆ ุงู†ุง ู…ู…ูƒู† ุงุดุชุฑูŠ ู…ู† ุงู„ุฃูˆู„ ู…ู† ุงู„ุฃูˆู„ .. ู…ู†

16
00:00:52,520 --> 00:00:58,680
ุงู„ุฃูˆู„ .. ูŠุนู†ูŠ practice ..

17
00:01:22,020 --> 00:01:29,160
ู…ุงุดูŠ ุจุดูˆู ูƒุฏู‡ ุงู† ุดุงุก ุงู„ู„ู‡ ู„ุฃ ู‡ุจุฏุฃ question number

18
00:01:29,160 --> 00:01:35,230
one ุฃู†ุง ุจุฏูŠ ุฃู‚ุฑุง ุงู„ุณุคุงู„ ุฃูู‡ู…ูƒ ุงู„ู…ุนู†ู‰ ุชุจุนู‡ูˆ ุงุนุฑููƒ

19
00:01:35,230 --> 00:01:38,290
ุงูŠุด ุงู„ keyboards ุงู„ู„ูŠ ุงุญู†ุง ุนุงูŠุฒูŠู†ู‡ุง ูŠุนู†ูŠ ูƒู„ู…ุงุช

20
00:01:38,290 --> 00:01:42,310
ุงู„ู…ูุชุงุญูŠุฉ ุงู„ู„ูŠ ู…ู† ุฎู„ุงู„ู‡ุง ุจุนุฑู ุงู„ุญู„ ูˆ ุจุนุฏูŠู† ุจู‚ุฏุฑ

21
00:01:42,310 --> 00:01:45,830
ุงุดูŠู„ ุฅุฌุงุจุงุช ู…ุด ุตุญูŠุญุฉ ูˆ ุชู… ุนูŠุฏู†ูŠ ู…ู…ูƒู† ุฅุฌุงุจุฉ ุงูˆ

22
00:01:45,830 --> 00:01:49,990
ุชู†ุชูŠู† ู‡ู…ุง ุงู„ุตุญ ูุจุฎุชุงุฑ ุงู„ correct answer ุงู„ sample

23
00:01:49,990 --> 00:01:53,150
distribution describe distribution of ุงุญู†ุง ุฃุฎุฏู†ุง

24
00:01:53,150 --> 00:01:56,830
ู‚ุจู„ ู‡ูŠูƒู… ุงู„ sample distribution ุจูŠุนู…ู„ distribution

25
00:01:56,830 --> 00:02:02,670
ู„ statistic ุงู…ุง ู‡ูŠูƒูˆู† ุงู„ sample meanุฃูˆ ุงู„ู€ sample

26
00:02:02,670 --> 00:02:05,970
of proportion ุฏูŠ ุดุฑุญ ุฎุจุท ุจูŠู†ู‡ ูˆุจูŠู† ุงู„ hypothesis

27
00:02:05,970 --> 00:02:08,830
ุงู„ hypothesis ุจูŠูƒูˆู† ุงู„ claim about the population

28
00:02:08,830 --> 00:02:11,650
parameter ู‡ู†ุงูƒ ุฅุฐุง ุงู†ุชุดุฑุช ุชุณุนุฉ ูƒู„ู…ุฉ ุนู† ุงู„

29
00:02:11,650 --> 00:02:14,450
population parameter ูŠุนู†ูŠ ุจุชูƒู„ู… ุนู† ุงู„ ู…ูŠูˆ ูˆุนู†

30
00:02:14,450 --> 00:02:17,960
ุงู„ุจูˆุนูŠููŠ ุงู„ุญู„ู‚ุฉ ุงู„ุณุงุจุนุฉ ุนู†ุฏู…ุง ู†ุชุญุฏุซ ุนู† ู…ุฌู…ูˆุนุฉ

31
00:02:17,960 --> 00:02:21,960
ู…ุฌู…ูˆุนุฉ ู†ุญู† ู†ุชุญุฏุซ ุนู† ู…ุฌู…ูˆุนุฉ ู…ุฌู…ูˆุนุฉ

32
00:02:21,960 --> 00:02:33,320
ุงู„ุงุณุชุงุชูŠุณุชูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒูŠูƒ

33
00:02:42,000 --> 00:02:44,680
both parameters and statistics ุทุจุนุง ู„ุฃ ูุงู„ุชุงู„ูŠ

34
00:02:44,680 --> 00:02:48,060
correct answer is C ุฅุฐุง ุงู„ first one C is correct

35
00:02:48,060 --> 00:02:53,180
I just want to double check if the answers I mean

36
00:02:53,180 --> 00:02:55,960
answer key is correct or not at the end of your

37
00:02:55,960 --> 00:02:59,440
book ุญู†ุชุฃูƒุฏ ุฅูŠู‡ ุจุณ ุตุญูŠุญ ูˆู„ุง ู„ุฃ ุงู„ correct answer

38
00:02:59,440 --> 00:03:05,340
is C which is correct number two true or .. ุฅุฐุง

39
00:03:05,340 --> 00:03:10,840
one C number two true or falseุงู„ู€ Sample

40
00:03:10,840 --> 00:03:15,780
Distribution is defined as a probability

41
00:03:15,780 --> 00:03:20,020
distribution of sample sizes that can be observed

42
00:03:20,020 --> 00:03:27,780
from a given population ุฑู‚ู… ุงุชู†ูŠู† ู…ุฑุฉ ุชุงู†ูŠุฉ ุงู„ู€

43
00:03:27,780 --> 00:03:29,940
Sample Distribution is defined as a probability

44
00:03:29,940 --> 00:03:34,260
distribution of possible sample sizes that can be

45
00:03:34,260 --> 00:03:38,250
observed ู‡ูˆ ุงู„ู€ Sample Distribution ูŠุนุทูŠุจูŠุนุทูŠู†ูŠ

46
00:03:38,250 --> 00:03:40,130
ุงู„ู€ mean ุงู„ู„ูŠ ู‡ูˆ ุงู„ู€ center ุจูŠุนุทูŠู†ูŠ ุงู„ spread

47
00:03:40,130 --> 00:03:45,350
ุจูŠุนุทูŠู†ูŠ ุงู„ shape ูุจุงู„ุชุงู„ูŠ ุงู† ู‡ูˆ .. ู‡ูˆ ุจูŠุญูƒูŠ ุชุนุฑูŠูู‡

48
00:03:45,350 --> 00:03:48,870
ุนุจุงุฑุฉ ุนู† probability of distribution ุทุจุนุง ู„ุฃ ู‡ูˆ

49
00:03:48,870 --> 00:03:51,610
ุจูŠุนุทูŠ ุงู„ center ุงูˆ ุงู„ spread ุงูˆ ุงู„ shape ูุจุงู„ุชุงู„ูŠ

50
00:03:51,610 --> 00:03:54,290
ุจูŠุนุทูŠุด probability ูƒ .. ู„ู…ุง ุจุญูƒูŠ ู„ูƒ ุงู„ X bar ุจุณูˆุงุฉ

51
00:03:54,290 --> 00:03:57,570
ุฎู…ุณูŠู† ู‡ู„ ุจูŠุนุทูŠู†ูŠ probability ู„ุฃ ุงุนุทุงู†ูŠ ุงู„ center

52
00:03:57,570 --> 00:04:02,230
ุชุจุนู‡ุง ุจุณูˆุงุฉ ุฎู…ุณูŠู† ูˆุงุถุญุŸ ุฅุฐุง ู„ู…ุง ุจุญูƒูŠ send

53
00:04:02,230 --> 00:04:06,440
distribution of X barุงู„ู‚ูŠู… ู‡ูˆ 16 ุฅุฐุง ูƒุงู†ุช ุงู„ู‚ูŠู…

54
00:04:06,440 --> 00:04:09,600
ุงู„ุตุญูŠุญุฉ 10 ู…ุงุนุทุงู†ูŠุด ุงู„ุจุฑุงุจูŠุฑูŠุง ุชุจุนู‡ุง ุชุนุทุงู†ูŠ ุงู„ู‚ูŠู…

55
00:04:09,600 --> 00:04:14,740
ู„ู„ู‚ูŠู… ุฃูˆ ุงู„ู‚ูŠู… ุงู„ุตุญูŠุญุฉ ุฃูˆ ุงู„ุดูƒู„ ู†ูุณู‡ุง ุฅุฐู† ุจูŠ is

56
00:04:14,740 --> 00:04:22,000
the correct answer ุฅุฐู† ุงุชู†ูŠู† ุจูŠ ุฑู‚ู… ุชู„ุงุชุฉ ุงู„ุชู„ุงุชุฉ

57
00:04:22,000 --> 00:04:24,640
ุจูŠุญูƒูŠ amount of time it takes to complete an

58
00:04:24,640 --> 00:04:29,090
examination has left skewed distributionุงู„ุฒู…ู† ุงู„ู„ูŠ

59
00:04:29,090 --> 00:04:33,630
ู„ุงุฒู… ุนุดุงู† ุชุญุณุจ it takes a complete examination

60
00:04:33,630 --> 00:04:38,630
ุชุฎู„ุต ุงู„ุงู†ุชุญุงู† ุฅูŠู‡ ุงู„ู„ูŠ ู‡ูˆ left skewedุŸ ุชูˆุฒูŠุน ู…ุด

61
00:04:38,630 --> 00:04:42,110
normal ุฅูŠู‡ ุงู„ู„ูŠ ู‡ูˆ ู„ูŠุดุŸ left skewed with a mean of

62
00:04:42,110 --> 00:04:46,290
65 minutes and standard deviation of 8 minutes if

63
00:04:46,290 --> 00:04:49,950
64 students were randomly sampled ุฃุฎุฏ ุนูŠู†ุฉ ูƒุจูŠุฑุฉ

64
00:04:49,950 --> 00:04:56,180
ูˆู„ุง ุตุบูŠุฑุฉุŸูƒุจูŠุฑุฉุŒ ุชุฐูƒุฑ ุงุญู†ุง ุญูƒูŠู†ุง ู„ู…ุง ุชูƒูˆู† ุนู†ุฏู‡ for

65
00:04:56,180 --> 00:04:59,540
most distributions ู„ู…ุง n is large, large enough it

66
00:04:59,540 --> 00:05:01,760
means greater than 30 then we can assume the

67
00:05:01,760 --> 00:05:04,600
popularly standard distribution of the standard

68
00:05:04,600 --> 00:05:08,140
mean is approximately normally distributedู„ูˆ ูƒุงู†ุช

69
00:05:08,140 --> 00:05:11,420
N ุฃูƒุจุฑ ู…ู† 30 ูˆุญูƒูŠู†ุง for fair distribution ู„ูˆ ูƒุงู†ุช

70
00:05:11,420 --> 00:05:15,980
N ุฃูƒุจุฑ ู…ู† 15 ููˆุงุถุญ ุงู„ุญุงู„ุฉ ุงู„ู„ูŠ ุนู†ุฏู‡ left skewed ูˆ

71
00:05:15,980 --> 00:05:19,620
ุงู„ sample size ุฃุฎุฏุช ุฃุฏูŠุงุด 64 ูŠุนู†ูŠ ุนุฏุงุฏู‡ุง ุฃูŠุงุด more

72
00:05:19,620 --> 00:05:23,800
than 30 more than 30 ุฅุฐุง we are okay we are sample

73
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the probability that the sample mean of the sample

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distribution exceeds 71 minutes is approximately

75
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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
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ู‡ูˆ ุนุงูŠุฒ ุงู„ mean ู„ุญุธุฉ ู…ุด ุจูŠุญูƒูŠ ุงู†ุง ู‡ุฐุง ู„ุฎุจุทูƒ ุฎุงุฑุฌ

78
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ุ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
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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
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ุงู„ู…ุซู„ุฉ ุฃู†ุง ุตุฑุช ู…ุด ุจุฑุญู„ ุงู„ู…ุซู„ุฉ ุฃู†ุง ูƒู†ุช ูุงูƒุฑ ุฃุญูƒูŠ

85
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ุงู„ุชูˆุฒูŠุน ุงู„ุทุจูŠุนูŠ ูˆู„ุง ู„ุฃ ุจุญุงูˆู„ูŠ ุนู„ู‰ ุงู„ Z ู…ุธุจูˆุท ุงู„ CZ

86
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ุ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

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ุฃุทู„ุน ู…ูŠู†ุŸ ุฃู‡ ุจุงู„ุธุจุท ุนุดุงู† ุฃุนุฑู ุฃุทู„ุน ุงู„ square root

89
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ุชูƒูˆู† ู…ุซู„ุง ุจุฏูŠู‡ุงุด calculator ู‡ุฐุง ุฅูŠุด ู‡ุชุณุงูˆูŠุŸ

90
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ู‡ุฏูˆู„ ุงู„ุจุตุด ู…ูˆุฌูˆุฏุŸsix ุจุนุฏูŠู† ุชู…ุงู†ูŠุฉ ุน ุชู…ุงู†ูŠุฉ ู…ุด ู‡ูŠูƒ

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ูŠุนู†ูŠ ุจุฏูˆุฑ ุนู„ู‰ P of Z ุฃูƒุจุฑ ู…ู† ุณุชุฉ Z ุฃูƒุจุฑ ู…ู† ุณุชุฉ ุงู‡

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ูˆุงุญุฏ ุจูŠุทู„ุน ูˆุงุญุฏ ู†ู‚ุต ูˆุงุญุฏ ูˆุงุญุฏ ู†ู‚ุต ุณูŠ ุงู‡ ู‡ุงูŠ ุงู„ุณุชุฉ

93
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ุงู„ุณุชุฉ ูˆูŠู† ุงู„ white side ุนู„ู‰ ููˆู‚ ุงู„ุนู„ุจูŠุฉุงู„ู€ tab

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ุงู„ู…ุนุทู‰ ุงู„ area ู„ูˆูŠู†ุŸ to the left ุทุจุนุง z ุงู„ area to

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00:07:21,740 --> 00:07:25,680
the left sideุŒ ู…ุธุจูˆุทุŸ ุงุฐุง this equals one minus b

96
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of z less than six ุงู„ tab ุงู„ู…ุนุทุงู†ูŠ ู„ุบุงูŠุฉ 3.4 ูˆ ุฌูˆ

97
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ู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
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.. ุ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
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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†

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approximately ู…ุซู„ุง ุงู‡ equal one ุงู‡ ุทุจุนุง ู„ุฃ ู‡ูŠ ุงู„

109
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equal one ู‡ุฐู‡ ู„ุฃู‚ู„ ู…ู† ุณุชุฉ equal one ุงู‡ ู„ุฃู‚ู„ ู„ุฃู‚ู„

110
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ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„

111
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ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„

112
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ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„

113
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ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„

114
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ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„ ู„ุฃู‚ู„

115
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ู„ุฃู‚

116
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ุฎู„ุตู†ุง ุชู„ุงุชุฉ ุงูŠู‡ุŸ ู…ุธุจูˆุท ู‡ูŠูƒุŸ ุงูŠู‡ ุงู„ุชู„ุงุชุฉ ุงูŠู‡ุŸ ุฑู‚ู…

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ุงุฑุจุนุฉ The

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distribution of the number of loaves of bread sold

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per week by large bakery over the past five years

120
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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
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ูƒุงู†ุช ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏ ู…ุฌุฑุฏHas been

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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
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ุฃูƒุจุฑ ู…ู† seven thousand eight hundred ninety five

128
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ุจุฏูˆุง ุงู„ mean ุฅูŠุด ุจูŠุณุงูˆูŠ ู†ูุณ ุงู„ุณุคุงู„ ุฏู‡ ุจุงู„ุธุจุท

129
00:10:08,430 --> 00:10:09,370
ุญุงูˆู„ูˆุง ู„ู„ z

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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
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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