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 34.8 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 single pilot is more important.

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

Answer 1

Given: mean = 138, sigma = 34.8

A. P( a< xbar < b) = P(xbar<b) - P(xbar <a)

Using,

P(xbar < ) =

P(130< xbar<171) = -

= -  

= 0.8289 - 0.4090

= 0.4199

Thus, there is 0.4199 Probability that weight is between 130lb and 171lb.

B. Using,

P(x < a) =

where mu = 138 , sigma = 34.8 , n = 37

P(130< xbar < 171) =

-

= -  

= -  

= 1 - 0.0808

= 0.9192

Thus, there is 0.9192 Probability that the weight is between 130lb and 171 lbs for 37 pilots.

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