Question 974232: 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 160 lb and a standard deviation of 27.5 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 place as needed.)
B.) If 39 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 place as needed.)
C) When redesigning the ejection seat which probability is more relevant
Part A or Part B
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! mean=160
sd =27.5
z=(150-160)/27.5 =-10/27.5= -.364.
z=(201-160)/27.5 = 41/27.5= 1.49
Want z-values between these two numbers. It is 0.5738
This increases the z-value by a factor of the sqrt (39)=6.245
(x-mean)/[sd/sqrt(39)] ;; Dividing, we invert, so all the above values are multiplied by 6.2449
z= -2.27
z= 9.30
probability is between these two values, which is almost 1.
Actual is 0.9884
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.
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