Answer:
99.85% of American women have shoe sizes that are less than 12.67
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 = 8.2
Standard deviation = 1.49
Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67
12.67 = 8.2 + 3*1.49
12.67 is 3 standard deviations above the mean.
Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above. Of those 50% above, 99.7% are between the mean and 12.67. So
0.5 + 0.997*0.5 = 0.9985
99.85% of American women have shoe sizes that are less than 12.67
