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An engineer is going to redesign an ejection seat for an airplane. The seat was

ID: 3208343 • Letter: A

Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 181. The new population of pilots has normally distributed weights with a mean of 127 lb and a standard deviation of 33.9 lb

a. If a pilot is randomly selected, find the probability that his weight is between120 lb and 181

The probability is approximately _______

b. If 35 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 181 lb.

The probability is approximately____

Explanation / Answer

Here it is given that distribution is normal with mean=127 and sd=33.9

a. We need to find P(120<x<181)=P(120-127/33.9<z<181-127/33.9)=P(-0.21<z<1.59)=0.5272

b. P(120<xbar<181)=P(120-127/(33.9/sqrt(35)<z<181-127/(33.9/sqrt(35)=P(-1.22<z<9.42)=0.8888