An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 126 lb and a standard deviation of 34.7 lb.

If a pilot is randomly selected, find the probability that his weight is between 120 lb and 171 lb.

The probability is approximately _______ (Round to four decimal places as needed).

To find the probability that a randomly selected plot's weight is between 120 ib and 171 ib, we need to calculate the z-scores for these weights and use the Z-table to find the corresponding probabilities. The probability is approximately 0.5305.

Explanation:

To find the probability that a randomly selected plot's weight is between 120 ib and 171 ib, we need to calculate the z-scores for these weights and use the Z-table to find the corresponding probabilities.

First, let's calculate the z-score for 120 ib:

z = (x - μ) / σ = (120 - 126) / 34.7 ≈ -0.1734

Next, let's calculate the z-score for 171 ib:

z = (x - μ) / σ = (171 - 126) / 34.7 ≈ 1.2964

Using the Z-table, we can find that the probability of a z-score between -0.1734 and 1.2964 is approximately 0.5305.