Question

Assume that military aircraft use ejection seats designed for men weighing between 131.9 lb and 208 lb. If​ women's weights are normally distributed with a mean of 167.1 lb and a standard deviation of 41.2 ​lb, what percentage of women have weights that are within those​ limits?

Are many women excluded with those​ specifications? The percentage of women that have weights between those limits is nothing​%. ​(Round to two decimal places as​ needed.)

Are many women excluded with those​ specifications?

A. ​Yes, the percentage of women who are​ excluded, which is the complement of the probability found​ previously, shows that about half of women are excluded.
B. ​Yes, the percentage of women who are​ excluded, which is equal to the probability found​ previously, shows that about half of women are excluded.
C. ​No, the percentage of women who are​ excluded, which is the complement of the probability found​ previously, shows that very few women are excluded.
D. ​No, the percentage of women who are​ excluded, which is equal to the probability found​ previously, shows that very few women are excluded.

Answer 1

To find the percentage of women with weights within the given limits, calculate the z-scores for the lower and upper weight limits, and find the area under the normal distribution curve between those z-scores. The percentage of women with weights between those limits is approximately 73.77%, suggesting that only a few women are excluded with those specifications.

Step-by-step explanation:

To find the percentage of women with weights that are within the given limits, we need to calculate the z-scores for the lower and upper weight limits and then find the area under the normal distribution curve between those z-scores.

First, we calculate the z-score for the lower weight limit: z = (lower limit - mean) / standard deviation = (131.9 - 167.1) / 41.2 = -0.8544.

Similarly, the z-score for the upper weight limit is: z = (upper limit - mean) / standard deviation = (208 - 167.1) / 41.2 = 0.9903.

Using a standard normal distribution table or a calculator, we can find the area between these two z-scores, which represents the percentage of women with weights within the given limits.

The percentage of women with weights between those limits is approximately 73.77%. This means that a large majority of women fall within the specified weight range, suggesting that only a few women are excluded with those specifications.