QuestionSuppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.19 and a standard deviation of 1.49 . Using the empirical rule, what percentage of American women have shoe sizes that are no more than 11.17 ? Please do not round your answer.

Studdy Solution
According to the empirical rule, approximately 95% of the data falls within 2 standard deviations of the mean in a normal distribution. Since we are looking for the percentage of women with shoe sizes no more than 11.17, which is 2 standard deviations above the mean, we consider the lower tail up to this point.
Since 95% of the data is within 2 standard deviations (from $-2\sigma$ to $+2\sigma$), and the distribution is symmetric, half of the remaining 5% is in the upper tail beyond $+2\sigma$.
Thus, the percentage of data below $+2\sigma$ is:
$95\% + \frac{5\%}{2} = 97.5\%$
The percentage of American women with shoe sizes no more than 11.17 is:
$$\boxed{97.5\%}$$