systistics question

Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.478.47 and a standard deviation of 1.51.5. Using the empirical rule, what percentage of American women have shoe sizes that are no more than 11.4711.47? Please do not round your answer.

Answer

Answer 1

Typically, "the empirical rule" means that + 1 standard deviation (from the mean) captures 68% of the data, + 2 standard deviations captures 95% of the data, and + 3 standard deviations captures 99.7% of the data. Like this:

So American women who have shoe sizes that are no more than 11.47 are those shaded. Add up the percentages to get the amount.