1. A Day of Classy Review

2. Shifting and Scaling SAT/ACT Max SAT: 1600 (old school) Max ACT: 36
SAT = 40 x ACT + 150
ACT Summary Stats:
Lowest = 19
Mean = 27
SD = 3
Q3 = 30
Median = 28
IQR = 6
Find equivalent SAT scores

3. SAT and ACT ACT Summary Stats: Lowest = 19 Mean = 27 SD = 3 Q3 = 30
Median = 28
IQR = 6
SAT = 40 x ACT + 150
𝐿𝑜𝑤𝑒𝑠𝑡 𝑆𝐴𝑇 =40 ∗19+150=910
𝑀𝑒𝑎𝑛 𝑆𝐴𝑇 =40 ∗27+150=1,230
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑆𝐴𝑇 =40∗3=120
𝑄3 𝑆𝐴𝑇 =40 ∗30+150=1,350
𝑀𝑒𝑑𝑖𝑎𝑛 𝑆𝐴𝑇 =40∗28+150=1,270
𝐼𝑄𝑅 𝑆𝐴𝑇 =40 ∗6=240

4. NormalCDF
The NormalCDF( function finds the percent of the total area of the distribution that falls between two z-scores.
For example, what would the
NormalCDF(-1,1) be?
(Hint: rule)

5. NormalCDF Procedure First, determine the type of question being asked
Once you’ve determined it is appropriate to use the NormalCDF function, convert given values into z-scores
𝑧= 𝑦− 𝑦 𝑆𝐷

6. NormalCDF Questions: Answers:
What percent of the distribution falls between X and Y?
What percent of the distribution is greater than Y?
What percent of the distribution is less than X?
Answers:
NormalCDF(X,Y)
NormalCDF(Y,99)
NormalCDF(-99,X)

7. invNormal( Going the Other Way
The invNormal( function finds what z-score would cut off that percent of the data
Example: What z-score cuts off the top 10% in a Normal model? The bottom 20%?
The trick here is figuring out what percent (as a decimal) to enter in to the function.
Imagine invNormal calculates the area starting at -99.
So to find the z-score that cuts off the top 10% we want the z-score that includes 90%
invNormal (.9) = 1.28

8. invNormal( Example
Based on the model N(1152, 84) describing angus steer weights, what are the cut-off values for
A) highest 10%
B) lowest 20%
C) middle 40%
A) invNormal(.9) = 1.28
B) invNormal(.2) = -.842
C) invNormal(.3) = -.524
invNormal(.7) = .524
1,259lbs
1,081lbs
1,108 – 1196lbs

9. New Topic – Normal Probability Plots
How to decide when the normal model (unimodal and symmetric) is appropriate:
Draw a picture (Histogram)
Draw a picture! (Normal Probability Plot)
A Normal Probability Plot is a plot of Normal Scores (z-scores) on the x-axis vs the units you were measuring on the y-axis (weights, miles per gallon, etc.)
A unimodal and symmetric distribution will create a straight line

10. What it Looks Like

11. What it Looks Like

12. How It Works
A Normal probability plot takes each data value and plots it against the z-score you would expect that point to have if the distribution were perfectly normal
These are best done on a calculator or with some other piece of technology because it can be tricky to find what values to “expect”

13. Homework
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