Check Homework. More with normal distribution
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1 More with normal distribution Wednesday, September 7, 2016 Warm-up Draw the models for each of the following: Assume adult male heights are normally distributed with mean 70 inches and standard deviation 4 inches. Assume also that adult female heights are normally distributed with mean 65 inches and standard deviation 3.5 inches. Check Homework
2 Warm-up Draw the models for each of the following: Assume adult male heights are normally distributed with mean 70 inches and standard deviation 4 inches. Assume also that adult female heights are normally distributed with mean 65 inches and standard deviation 3.5 inches.
3 Am I tall or short?
4 Standardized Score OR Z-score Ms. Blunt Height: Z-score: Mr. Oehlert Height: Z-score:
5 Percentile Using the table
6 Given N(70, 4) inches Find the z-scores for the following men Ben Stiller: 66.5 inches Justin Timberlake: 73 inches Let s find their individual percentiles Find the percentage of people between Ben Stiller and Justin Timberlake Slide 6-7
7 Given the following Normal distribution of women s heights: N(65, 3.5) find the z-score and percentile for each of these women. What percent of women are between them in height? Blake Lively 70 Hayden Panettiere 60 Slide 6-8
8 How tall are these actresses? Drew Barrymore th percentile Uma Thurman th percentile
9 How tall are these actors? Dwayne Johnson th percentile Kevin Hart 6.68 th percentile
10 Practice A town s January high temperatures average 36 F with a standard deviation of 10. What is the z-score this month of 55? That same town has a mean in July of 74 and a standard deviation of 8. What is the z-score this month of a temperature of 55. In which month is 55 more uncommon? How do you know?
11 More Practice An incoming freshman took her college s placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12. On which exam did she do better compared with other freshmen?
12 Let s look at some data Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S. Department of Agriculture Using the calculator Create a dot plot Find the mean & standard deviation Find the median & IQR Slide 6-13
13 Let s adjust the data Inflation Add 3 cents to each price What happens to Distribution shape? Mean? Standard Deviation? Median? IQR? Slide 6-14
14 Let s rescale To a different currency Approximate to Canadian Dollars: (x 1.3) What happens to The shape of the distribution? Measures of center? Measures of spread? Slide 6-15
15 Standardizing data into z-scores shifts the data by subtracting the mean and rescales the values by dividing by their standard deviation. What happens to the shape? Standardizing into z-scores does not change the shape of the distribution. What happens to the center? Standardizing into z-scores changes the center by making the mean 0. What happens to the spread? Standardizing into z-scores changes the spread by making the standard deviation 1. Slide 6-16
16 Homework Page (37-42)
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