Answer:
2.5% of American women have shoe sizes that are at least 11.03.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 8.11
Standard deviation = 1.46
Using the empirical rule, what percentage of American women have shoe sizes that are at least 11.03?
11.03 = 8.11 + 2*1.46
So 11.03 is two standard deviations above the mean.
The empirical rule states that 95% of the measures are within 2 standard deviation of the mean. Since the distribution is symetric, of those 5% farther than two standard deviations of the mean, 2.5% are higher than 2 standard deviations above the mean and 2.5% are lower than 2 standard deviations below the mean.
So 2.5% of American women have shoe sizes that are at least 11.03.
