Chapter 7.2-7.3: Z-scores and Probabilities - Healthcare Perspective
Channel: Monika Wahi
Date: 2015-11-02

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In this video, Monika Wahi lectures to Laboure College students in her Essentials of Statistics class. 
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I listed the links I mention below as they come up in the lecture. Enjoy!

00:20 Lecture learning objectives
00:44 Topics covered in the lecture
01:14 Review of Empirical Rule diagram – what about in-between the cutpoints?
02:20 Definition of z-score
02:47 Analogy of a z-score standard: mapping currency to the US dollar for comparisons
03:32 What is needed to convert x’s to z-scores
04:08 Introduction of z-score formulas
04:23 Smart friend example: calculating z-score
06:41 Not-so-smart friend example: calculating z-score
07:45 Reviewing probabilities from the Empirical Rule diagram – how do you find the probabilities in-between the cutpoints?
08:37 Relating the z-score probabilities to areas under the curve in the Empirical Rule diagram
09:50 General description of what is in the z table
10:48 Guide to reading the z table
11:39 How to navigate the z table, and example of looking up negative z (areas to the left of z) in z table to find probability.
14:03 Interpreting the probability we looked up. Because the area was to the left of z, we take the probability “directly”.
14:31 Explanation of what to do with smart friend example, when looking up areas to the right of z. Description of two approaches: Subtract from 1, and look up opposite z.
15:25 Example of looking up probability for positive z in the table.
15:54 Subtracting probability we found from 1, and interpreting it.
17:10 Demonstration of the second way – looking up the opposite z (which is negative) in the table.
17:36 Explanation as to why the opposite z probability was the same as the “subtract from 1” probability we got
18:08 Monika’s tip: Draw a picture and do a reality check for whatever you calculate as your probability
19:37 Introduction to calculating probabilities between two z scores
19:52 Steps to calculating probabilities between two z scores, and explanation of x1 and x2 (and z1 and z2)
21:25 Demonstration of calculating the probabilities in the two tails, then subtracting them from the whole to get the middle probability
22:08 Demonstration of looking for a probability greater than 50% (e.g., probability of scoring above the not-so-smart student) – applying both methods of looking of up an area to the right of z
23:11 Demonstration of looking for probability will score below smart student (greater than 50%)
23:37 Note about z table values below -3.49 and above 3.49
24:27 Introduction to calculating x when z is given
24:46 Strategy of back-calculating z from probability, and x from z using the formula
25:25 Example working out a question finding x for a given z
26:29 Example working out a question finding x for a given probability
26:56 How to look up z from a given probability in the z table
28:21 Using z in the equation to find x as the cutpoint for the top % of scores
29:18 Similar example to find x as the cutpoint for the bottom % of scores
31:29 Similar example to find x1 and x2 cutpoints for a given middle probability
33:33 Tips for what to do if you panic on a z-score test, game-show style
36:13 Final tips and tricks for getting z-scores right
38:51 Review of lecture topics and conclusion

Chapter 7.2-7.3: Z-scores and Probabilities - Healthcare Perspective