Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, we have a value that is more than 5 standard deviations below the mean. Using the formula for z-score, we have:
z = (x - mu) / sigma
z = (3.46 - 8.05) / 1.53
z = -2.98
According to the empirical rule, almost all of the data falls within three standard deviations, so the percentage of American women with shoe sizes less than 3.46 is approximately:
0.15%
Explanation: