Prob and Stat Homework help

Question

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

130 lb and a standard deviation of 31.8 lb.

Question content area bottom

Part 1 a. If a pilot is randomly​ selected, find the probability that his weight is between 120 lb and 171 lb.

The probability is approximately :

.

Part 2 b. If 38 different pilots are randomly​ selected, find the probability that their mean weight is between 120 lb and 171 lb.

The probability is approximately :

Answer 1

Thanks for asking,

Part a), we want P(120<X<171),

Step 1, standardization to z scores

For 120 lb: 𝑍_1 = (120 − 130)/31.8​ = −0.3145

For 171 lb: 𝑍_2 = (171 − 130)/31.8 = 1.2899

Step 2, Use the standard normal distribution table.

Φ( − 0.3145 ) ≈ 0.3766

Φ ( 1.2899 ) ≈ 0.9017

Step 3: Subtract to find the probability. 𝑃 ( 120 < 𝑋 < 171 ) = 0.9017 − 0.3766 = 0.5251

I will answer part b shortly.