Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.43 and a standard deviation of 1.5. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.93 and 9.93?

a. 68%
b. 95%
c. 99.7%
d. 84%

Answer 1

Approximately 68% of American women's shoe sizes fall between 6.93 and 9.93 according to the empirical rule for a bell-shaped distribution since this range covers one standard deviation above and below the mean shoe size (8.43).

Step-by-step explanation:

Using the empirical rule for a bell-shaped distribution, we can determine the percentage of American women's shoe sizes that fall between 6.93 and 9.93. The rule states that about 68% of the data lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In this case, the range between 6.93 and 9.93 is exactly one standard deviation below and one standard deviation above the mean shoe size (8.43 - 1.5 = 6.93; 8.43 + 1.5 = 9.93). Therefore, according to the empirical rule, approximately 68% of American women have shoe sizes that fall within this range.

The correct answer to the student's question is (a) 68%.