Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.52. Using the empirical rule, what percentage of American women have shoe sizes that are at least 12.6? Please do not round your answer.

0.15 % of American women have a shoe size greater than 12.6

Explanation:

*See the attached photo.

The percentage of American women that have shoe sizes that are at least 12.6 is; 0.0015

We are given;

Mean; x' = 8.04

Standard deviation; σ = 1.52

Using the empirical rule, we can have the data either 1, 2 or 3 standard deviations from the mean.

Thus;

At 1 standard deviation from mean, we have;

8.04 ± 1(1.52)

⇒ (6.52, 8.56)

At 2 standard deviations from the mean, we have;

8.04 ± 2(1.52)

⇒ (5, 11.08)

At 3 standard deviations from the mean, we have;

8.04 ± 3(1.52)

⇒ (3.48, 12.6)

We can see that the one with at least 12,6 is 3 standard deviations from the mean which from empirical rule is 99.7%

Thus;

percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%

P(x ≥ 12.6) = 0.15% = 0.0015

Read more about the empirical rule at; link

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