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# A Day of Classy Review PowerPoint PPT Presentation

A Day of Classy Review. 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. SAT and ACT. ACT Summary Stats: Lowest = 19 Mean = 27 SD = 3

A Day of Classy Review

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## A Day of Classy Review

### 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

### SAT and ACT

• ACT Summary Stats:

• Lowest = 19

• Mean = 27

• SD = 3

• Q3 = 30

• Median = 28

• IQR = 6

• SAT = 40 x ACT + 150

### 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: 68-95-99.7 rule)

### 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

### NormalCDF

• Questions:

• 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?

• NormalCDF(X,Y)

• NormalCDF(Y,99)

• NormalCDF(-99,X)

### 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

### 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

### 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

### 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”

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