An engineer is going to redesign an ejection seat for an airplane. The seat was
ID: 3365332 • Letter: A
Question
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150150 lb and 211211 lb. The new population of pilots has normally distributed weights with a mean of 160 lb160 lb and a standard deviation of 32.8 lb32.8 lb. a. If a pilot is randomly selected, find the probability that his weight is between 150150 lb and 211211 lb. The probability is approximately nothing. (Round to four decimal places as needed.) b. If 3737 different pilots are randomly selected, find the probability that their mean weight is between 150150 lb and 211211 lb. The probability is approximately nothing. (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 sample of pilots is more important. B. Part (a) because the seat performance for a single pilot is more important. C. Part (b) because the seat performance for a sample of pilots is more important. D. Part (b) because the seat performance for a single pilot is more important. Click to select your answer(s).
Explanation / Answer
mean=160
sd = 32.8
a) z=(150 - 160)/32.8 = - 0.305
z = (211-160)/32.8 = 1.55
Want z-values between these two numbers. P = 0.5511
b) This increases the z-value by a factor of the sqrt (37) = 6.08
(x-mean)/[sd/sqrt(37)] ;; Dividing, we invert, so all the above values are multiplied by 6.08
z= - 1.85
z= 9.42
probability is between these two values, which is almost 1.
Actual is 0.9884
c)The seat for each pilot matters a great deal. Having written that, if there is a standard deviation that high, the seat's tolerance must be at least 55 pounds on each side of the mean, or the selection process must be stricter. If the tolerance is that great to accommodate an individual pilot, it will certainly accommodate a large sample of pilots.
Part (b) because the seat performance for a single pilot is more important