An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 135 and a standard deviation of 25.1 lb. If a pilot is randomly selected find the probability that his weight is between 130 lb and 181 lb.

z= (130 -135)/25.1

z =
z = (181- 135)/25.1
z =

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the two Z scores.

it diffcult to answer

To find the probability that a randomly selected pilot's weight is between 130 lb and 181 lb, we need to use the concept of the standard normal distribution.

1. Convert the given weights to standard deviations.
- Subtract the mean weight from each of the given weights.
- Lower weight: 130 lb - 135 lb = -5 lb
- Upper weight: 181 lb - 135 lb = 46 lb
- Divide each result by the standard deviation.
- Lower weight: -5 lb ÷ 25.1 lb = -0.1992
- Upper weight: 46 lb ÷ 25.1 lb = 1.8355

2. Look up the cumulative probability for each standard deviation.
- Using a standard normal distribution table or a calculator, find the cumulative probability associated with each standard deviation.
- Cumulative probability for -0.1992: 0.4207 (rounded to four decimal places)
- Cumulative probability for 1.8355: 0.9666 (rounded to four decimal places)

3. Subtract the lower cumulative probability from the upper cumulative probability to find the probability that a randomly selected pilot's weight is between 130 lb and 181 lb.
- Probability = Upper cumulative probability - Lower cumulative probability
- Probability = 0.9666 - 0.4207 = 0.5459 (rounded to four decimal places)

Therefore, the probability that a randomly selected pilot's weight is between 130 lb and 181 lb is approximately 0.5459.