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A Day of Classy Review

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

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A Day of Classy Review

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  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

  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: 68-95-99.7 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

  6. 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? • 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. Page 136-141 # 3, 5, 12, 17, 28, 30 Homework

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