Range of women’s heights. In Chance (Winter 2007), Yale Law School professor Ian Ayres published the results of a study he conducted with his son and daughter on whether college students could estimate a range for women’s heights. The students were shown a graph of a normal distribution of heights and were asked, “The average height of women over 20 years old in the United States is 64 inches. Using your intuition, please give your best estimate of the range of heights that would include C% of women over 20 years old. Please make sure that the center of the range is the average height of 64 inches.” The value of C was randomly selected as 50%, 75%, 90%, 95%, or 99% for each student surveyed.

a. Give your estimate of the range for C = 50% of women’s heights.

b. Give your estimate of the range for C = 75% of women’s heights.

c. Give your estimate of the range for C = 90% of women’s heights.

d. Give your estimate of the range for C = 95% of women’s heights.

e. Give your estimate of the range for C = 99% of women’s heights.

f. The standard deviation of heights for women over 20 years old is known to be 2.6 inches. Use this information to revise your answers to parts a–e.

g. Which value of C has the most accurate estimated range? (Note: The researchers found that college students were most accurate for C = 90% and C = 95%.)