An engineer is going to redesign an ejection seat for an airplane. The seat was
ID: 3245109 • Letter: A
Question
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 161 lb. The new population of pilots has normally distributed weights with a mean of 130 lb and a standard deviation of 30.9 lb a. If a pilot is randomly selected find the probability that his weight is between 120 lb and 161 lb The probability is approximately (Round to four decimal places as needed) b. If 31 different pilots are randomly selected find the probability that their mean weight is between 120 lb and 161 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 single pilot is more Important B. Part (a) 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 D. Part (b) because the seat performance forExplanation / Answer
a)
P(120 < X <161) = P(X<161) - P(X<120)
= P(Z < 161-130/30.9) - P(Z < 120-130/30.9)
= P(Z < 1.003) - P(Z < -0.3236)
= 0.8421 - 0.3731
= 0.469
b)
P(120 < X <161) = P(X<161) - P(X<120)
= P(Z < 161-130/30.9/sqrt(31)) - P(Z < 120-130/30.9/sqrt(31) )
= P(Z < 5.5858) - P(Z < -1.8019)
= 1 - 0.0358
= 0.9642
c)
the correct choice is C)