Suppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.47 and a standard deviation of 1.5 . using the empirical rule, what percentage of american women have shoe sizes that are no more than 11.47 ? do not round your answer.

Solution: We are given that the shoe sizes of American women have a normal distribution, with mean, standard deviation

We have to find the percentage of American women whose shoe size's are not more than 11.47 P(x<11.47).

We need to first find the z-score.

Now we have to find . Using the empirical rule, we know that 97.5% data lies below 2 standard deviations above mean.

Therefore, using the empirical rule, 97.5% of American women have shoe sizes that are no more than 11.47.