An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 156 lb and a standard deviation of 29.4 lb.

a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.

To find the probability that a pilot's weight is between 150 lb and 201 lb, calculate the z-scores for these weights using the mean and standard deviation. Use the z-table to find the probabilities for the z-scores. Subtract the lower probability from the higher probability to find the final probability.

Explanation:

To find the probability that a pilot's weight is between 150 lb and 201 lb, we need to calculate the z-scores for these weights and then use the z-table.

The z-score formula is:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For the lower weight, z = (150 - 156) / 29.4 = -0.2041

For the upper weight, z = (201 - 156) / 29.4 = 1.5299

Using the z-table, we can find the probability for each z-score.

The probability for z = -0.2041 is 0.4207 and the probability for z = 1.5299 is 0.9389.

To find the probability between these two z-scores, we subtract the lower probability from the higher probability:

0.9389 - 0.4207 = 0.5182

So, the probability that a pilot's weight is between 150 lb and 201 lb is approximately 0.5182.