An engineer is going to redesign an ejection seat for an airplane. The seat was
ID: 3133596 • Letter: A
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 157 lb and a standard deviation of 29.2 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 _____
b. If 36 different pilots are randomly selected, find the probability that their mean weight is between
150 lb and 191 lb.
The probability is approximately _____
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.
Your answer is correct.
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.
Explanation / Answer
a)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 150
x2 = upper bound = 201
u = mean = 157
s = standard deviation = 29.2
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.239726027
z2 = upper z score = (x2 - u) / s = 1.506849315
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.405271328
P(z < z2) = 0.934075357
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.528804029 [ANSWER]
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b)
We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as
x1 = lower bound = 150
x2 = upper bound = 201
u = mean = 157
n = sample size = 36
s = standard deviation = 29.2
Thus, the two z scores are
z1 = lower z score = (x1 - u) * sqrt(n) / s = -1.438356164
z2 = upper z score = (x2 - u) * sqrt(n) / s = 9.04109589
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.075166512
P(z < z2) = 1
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.924833488 [ANSWER]
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c)
Only 1 pilot sit at the seat. Hence,
OPTION B: B.Part (a) because the seat performance for a single pilot is more important.