Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 159 lb and a standard deviation of 26.6 lb.

A. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 201 lb.The probability is approximately______?

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

B. If 40 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 201 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​ (a) because the seat performance for a single pilot 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​ (b) because the seat performance for a sample of pilots is more important.

Answer 1

A) = 159 lb

= 26.6 lb

P(X < A) = P(Z < (A - )/)

P(weight is between 150 lb and 201 lb for a single pilot) = P(150 < X < 201)

= P(X < 201) - P(X < 150)

= P(Z < (201 - 159)/26.6) - P(Z < (150 - 159)/26.6)

= P(Z < 1.58) - P(Z < -0.34)

= 0.9429 - 0.3669

= 0.5760

B) For sampling distribution of mean,

P( < A) = P(Z < (A - )/)

Sample size, n = 40

= = 159 lb

=

=

= 4.206

P(mean weight is between 150 lb and 201 lb for a sample of 40 pilots) = P(150 < < 201)

= P( < 201) - P( < 150)

= P(Z < (201 - 159)/4.206) - P(Z < (150 - 159)/4.206)

= P(Z < 9.99) - P(Z < -2.14)

= 1 - 0.0162

= 0.9838

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