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

Question

29. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 147 lb and a standard deviation of 27.8 lb a. If a pilot is randomly selected, find the probability that his weight is between 140 ib and 201 lb. The probability is approximately b. If 34 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 tb The probability is approximately c. When redesigning the ejection seat, which probability is more relevant? O A. Part (b) because the seat performance for a single pilot is more important. (Round to four decimal places as needed.) (Round to four decimal places as needed.) 0 B. Part (b) because the seat performance for a sample of pilots is more important ° C. Part (a) because the seat performance for a single pilot is more important. 0 D. Part (a) because the seat performance for a sample of pilots is more important.

Explanation / Answer

29)

a) probability=P(140 <X<201)=P((140-147)/27.8<Z<(201-147)/27.8)=P(-0.2518<X<1.9424)=0.9740-0.4006 =0.5734

b)for n=34 ; std error =std deviaiton/(n)1/2 =27.8/(34)1/2 =4.768

henc eprobability=P(140<X<201)=P((140-147)/4.768<Z<(201-147)/4.768)=P(-1.4682<X<11.3263)

=1-0.0710 =0.9290

c)option C is correct

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