An engineer is going to redesign an ejection seat for an airplane. The seat was
ID: 3133785 • Letter: A
Question
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 150 lb and a standard deviation of 32.2 lb. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 191 lb. The probability is approximately (Round to four decimal places as needed.) If 36 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 191 lb. The probability is approximately (Round to four decimal places as needed.) When redesigning the ejection seat, which probability is more relevant? Part (b) because the seat performance for a single pilot is more important. Part (a) because the seat performance for a single pilot is more important. Part (a) because the seat performance for a sample of pilots is more important. Part (b) because the seat performance for a sample of pilots is more important.Explanation / Answer
Using central limit theorem the sampling distribution of sample mean is normally distributed with mean mu and standard deviation sigma/root over n.
a.For X=140, z=(x-mu)/sigma=(140-150)/32.2=-0.31
For X=191, z=(191-150)/32.2=1.27
Thus P(140<X<191)
=P(X<191)-P(X<140)
=P(z<1.27)-P(z<-0.31)
=0.8980-0.3783
=0.5197
b.For 36 pilots the mean is 150 and sd=32.2/root over 36=5.37
For X=140, z=(x-mu)/sigma=(140-150)/5.37=-1.86
For X=191, z=(191-150)/5.37=7.63
Thus P(140<X<191)
=P(X<191)-P(X<140)
=P(z<7.63)-P(z<-1.86)
=1-0.0314
=0.9686
C.D)Part b) because the seat performance of sample of pilots is more important.