Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.438.43 and a standard deviation of 1.51.5. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.936.93 and 9.939.93

Answer 1

The right solution is "68%".

Explanation:

The empirical rule is:

`X\sim N(8.43, 1.5)`

According to the question,

=
`P(6.93< \mu < 9.93)`

=
`P((6.93-8.43)/(1.5) < (\mu -8.43)/(1.5) < (9.93-8.43)/(1.5) )`

=
`P(z(1)-P(z(-1))`

=
`68` (%)

Thus the above is the right solution.