Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.05 and a standard deviation of 1.53. Using the empirical rule, what percentage of American women have shoe sizes that are less than 3.46? Please do not round your answer.

Answer 1

Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, we have a value that is more than 5 standard deviations below the mean. Using the formula for z-score, we have:

z = (x - mu) / sigma

z = (3.46 - 8.05) / 1.53

z = -2.98

According to the empirical rule, almost all of the data falls within three standard deviations, so the percentage of American women with shoe sizes less than 3.46 is approximately:

0.15%

Explanation: