Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.15 and a standard deviation of 1.47 . Using the empirical rule, what percentage of American women have shoe sizes that are greater than 9.62? Please do not round your answer.

Step 1 ：Given that the shoe sizes of American women have a bell-shaped distribution with a mean of 8.15 and a standard deviation of 1.47.

Step 2 ：We are asked to find the percentage of American women who have shoe sizes greater than 9.62.

Step 3 ：First, we need to find how many standard deviations away from the mean 9.62 is. This is done by subtracting the mean from 9.62 and dividing by the standard deviation, which gives us a z-score.

Step 4 ：\(z = \frac{9.62 - 8.15}{1.47} \approx 1\)

Step 5 ：The z-score is approximately 1, which means that the shoe size of 9.62 is approximately one standard deviation away from the mean.

Step 6 ：According to the empirical rule, 68% of the data falls within one standard deviation of the mean, which means that 32% of the data falls outside of one standard deviation from the mean.

Step 7 ：Since we are looking for the percentage of women with shoe sizes greater than 9.62, and 9.62 is greater than the mean, we are interested in the upper half of this 32%, which is 16%.

Step 8 ：Final Answer: The percentage of American women who have shoe sizes greater than 9.62 is approximately \(\boxed{16\%}\).