Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.15 and a standard deviation of 1.52. Using the empirical rule, what percentage of American women have shoe sizes that are less than 11.19

Answer 1

Answer:

97.5% of American women have shoe sized less than 11.19

Step-by-step explanation:

Here, we want to use the empirical rule to find the percentage of women with shoe sizes less than 11.19

The first thing we shall do here is to find the z-score

Mathematically, that will be calculated using the formula;

z = (x-mean)/SD

z = (11.19-8.15)/1.52

z = 2

We can see that the given value is 2 standard deviation away to the right of mean

So, we want to get the percentage that is between the mean and two standard deviations away from it using the empirical rule

So according to the empirical rule

The percentage will be

100-2.35-0.15

= 100-2.5 = 97.5%