Please show work and formula used. An engineer is going to redesign an ejection
ID: 3181344 • Letter: P
Question
Please show work and formula used.An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing pilots weighting between 130 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 32.9 lb. The probability is approximately 0.5425. b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 191 lb. The probability is approximately 0.9211. 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 (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 for a single pilot is more important.
Explanation / Answer
a) = 138
= 30.3
standardize x to z = (x - ) /
P( 130 < x < 191) = P[( 130 - 138) / 30.3 < Z < ( 191 - 138) / 30.3]
P( -0.264 < Z < 1.7492) = 0.9599 - 0.3974 = 0.5625
(From Normal probability table)
The probability is approximately 0.5625.
b)Mean = 138
Standard deviation = 30.3
Standard error / n = 30.3 / 35 = 5.1216348
standardize xbar to z = (xbar - ) / ( / n )
P( 130 < xbar < 191) = P[( 130 - 138) / 5.121635 < z < ( 191 - 138) / 5.121635]
P( -1.562 < z < 10.3483) = 1.0000 - 0.0594 = 0.9406
(from normal probability table)
The probability is approximately 0.9406.
c)Go with option A as in problem(b)we went with sample.