Question

Use the empirical rule to answer the following question. The heights of American men have an approximately bell-shaped distribution with a mean of 70 inches (5' 10") and standard deviation of 3 inches. What is the percentage of American men whose height is between 61 and 79 inches (5' 1" and 6' 7")?

A) 99.7%
B) 68%
C) 95%
D) 84%

Answer 1

The percentage of American men whose height is between 61 and 79 inches is approximately 99.7%.

Step-by-step explanation:

The heights of American men follow a bell-shaped distribution, also known as a normal distribution. To determine the percentage of American men whose height is between 61 and 79 inches, we can use the empirical rule. The empirical rule states that for a normal distribution, approximately:

1. 68% of the data falls within 1 standard deviation of the mean
2. 95% of the data falls within 2 standard deviations of the mean
3. 99.7% of the data falls within 3 standard deviations of the mean

Since the mean height is 70 inches and the standard deviation is 3 inches, the range of 61-79 inches falls within 3 standard deviations from the mean. Therefore, the percentage of American men whose height is between 61 and 79 inches is approximately 99.7%, which is option A.