Question

The heights of all women in the United States are known to be normally distributed with a mean of 58 inches and standard deviation of 2.9 inches. The U.S. Navy requires that fighter pilots have heights between 56 inches and 69 inches. Find the percentage of women in the United States that meet this height requirement. Round the solution to two decimal places, if necessary.

Answer 1

Approximately 99.88% of women in the United States meet the height requirement for fighter pilots.

Step-by-step explanation:

The percentage of women in the United States that meet the height requirement for fighter pilots can be found using the standard normal distribution table. First, we need to convert the lower and upper limits of the height requirement to z-scores. The z-score formula is given by z = (x - µ) / σ, where x is the value, µ is the mean, and σ is the standard deviation.

For the lower limit of 56 inches, the z-score is z = (56 - 58) / 2.9 = -0.69. For the upper limit of 69 inches, the z-score is z = (69 - 58) / 2.9 = 3.79. We can then use the standard normal distribution table to find the percentage of women within this range.

From the table, the percentage of women within the range is approximately 99.88%. Therefore, approximately 99.88% of women in the United States meet the height requirement for fighter pilots.