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 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.

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Presentation on theme: " 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."— Presentation transcript:

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

3  ACT Summary Stats:  Lowest = 19  Mean = 27  SD = 3  Q3 = 30  Median = 28  IQR = 6  SAT = 40 x ACT + 150

4  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  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

6  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?  Answers:  NormalCDF(X,Y)  NormalCDF(Y,99)  NormalCDF(-99,X)

7  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  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) =  C) invNormal(.3) = invNormal(.7) =.524 A) 1,259lbs B) 1,081lbs C) 1,108 – 1196lbs

9  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

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12  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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