Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.11 and a standard deviation of 1.46. Using the empirical rule, what percentage of American women have shoe sizes that are no more than 5.19? Please do not round your answer.

Answer 1

To calculate this, we first need to determine how many standard deviations away 5.19 is from the mean:

Z = (X - μ) / σ
Z = (5.19 - 8.11) / 1.46
Z = -1.92

Using the empirical rule, we know that:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.

Since 5.19 is less than 1 standard deviation below the mean, we can estimate that approximately 84% of American women have shoe sizes that are no more than 5.19.