Download Name_________________________ Review Problems 5.11

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Review Problems
5.11 Heights of young women The distribution of the heights of young women aged 28 to 24 is approximately normal
with mean 65 inches and standard deviation 2.5 inches.
a) What percent of woman are at least 60 inches tall?
b) What percent are taller than 72 inches?
c) What is the height of the 75th percentile?
5.13 Heights of young women Sketch a picture of a normal curve from the above information and then use the 68-9599.7 rule to show what range of heights are represented in different proportions of the population.
5.15 More NCAA rules The NCAA considers a student a “partial qualifier” eligible to practice and receive an athletic
scholarship, but not to compete, if the combined SAT score is at least 720. The SATs scores are approximately normal
with a mean of 1017 and a standard deviation of 209. Find the percent of all SAT scores that are less than 720.
5.17 Women’s SAT scores The average performance of women on the SAT, especially the math part is lower than that of
men. The reasons for this gender gap are controversial. In 1999, women’s scores on the math SAT followed a normal
distribution with mean 495 and standard deviation 109. The mean for men was 531. What percent of women scored
higher than the male mean?
5.21 Normal curve properties, II Explain why the point one standard deviation below the mean in a normal distribution
is always the 16th percentile. Explain why the point two standard deviations above the mean is the 97.5th percentile.
5.23 Are we getting smarter? When the Stanford-Binet “IQ test” came into use of 1932, it was adjusted so that scores
for each age-group of children followed roughly the normal distribution with mean 100 and standard deviation 15. The
test readjusted from time to time to keep the mean at 100. If present-day American children took the 1932 StanfordBinet test, their mean score would be about 120. The reasons for the increase in IQ over time are not known but
probably include better childhood nutrition and more experience taking tests.
a) IQ scores above 130 are often called “very superior.” What percent of children had very superior scores in 1932?
b) If present-day children took the 1932 test, what percent would have very superior scores? (Assume that the standard
deviation 15 does not change.)
5.25 Potatoes Bags of potatoes in a shipment averaged 10 pounds with a standard deviation of 0.5 pounds. A histogram
of these weights followed a normal curve quite closely.
a) What percent of the bags weighed less than 10.25 pounds?
b) What percent weighed between 9.5 and 10.25 pounds?
5.27 Textbook costs Students taking an introductory statistics class in fall 2000 reported spending an average of $205 on
textbook that quarter with a standard deviation of $90. A rough sketch of a curve that fitted the histogram looked like:
a) Approximately what percent of the students spent between $115 and $295 on textbooks that quarter?
b) One student spent $187 on textbooks. What was her standard score? What percent of the students spent less
than she did on textbooks that quarter?
c) Explain why the sketch of the histogram above is important to your calculations.
Solutions:
11. a) 2.28% b) 0.26% c) 66.686
13. 68% between 62.5 and 67.5, etc.
15. 7.78%
17. 37.07%
21. explain the details of the 68-95-97.7 rule
23. a) 2.28 b)25.25%
25. a) 69% b)53.3%
27. a) 68% b) 42% c) approximately normal