Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 31.6 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 130 lb and 171 lb.

The probability is approximately ?

​(Round to four decimal places as​ needed.)

b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 130 lb and 171 lb.

The probability is approximately = ?

​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?

A.

Part​ (b) because the seat performance for a sample of pilots is more important.

B.

Part​ (b) because the seat performance for a single pilot is more important.

C.

Part​ (a) because the seat performance for a sample of pilots is more important.

D.

Part​ (a) because the seat performance for a single pilot is more important.

Answer 1

Solution :

Given that ,

mean = = 138

standard deviation = = 31.6

Using z table,  

(A)P(130< x <171 ) = P[(130 - 138) /31.6 < (x -) / < (171 - 138) /31.6 )]

= P( -0.25< Z <1.04 )

= P(Z <1.04 ) - P(Z < -0.25)

Using z table,  

= 0.8508 -0.4013

= 0.4495

n = 37

= 138

=  / n = 31.6 / 37=5.1950

P(130< <171 ) = P[(130 - 138) /5.1950 < ( - ) / < (171 - 138) /5.1950 )]

= P( -1.54< Z < 6.35)

= P(Z <6.35 ) - P(Z <-1.54 )

Using z table,  

= 1 - 0.0618

=0.9382