If the mean time between in-flight aircraft engine shutdowns is 12,500 operating hours, the 90^th percentile of waiting times to the next shutdown will be: A)20,180 hours. B)28,782 hours. C)23,733 hours. D)18,724 hours.

Question

Quizplus · Accepted Answer

To find the waiting time to the next shutdown that corresponds to the given percentile, we can use the exponential distribution with mean (or average) time between shutdowns of 12,500 operating hours. The formula for the cumulative distribution function (CDF) of the exponential distribution is:

F(x) = 1 - e^(-λx)

where λ is the rate parameter (the reciprocal of the mean) and e is the base of natural logarithm.

We need to find the value of x (the waiting time) such that F(x) = 0.901 (the 90th percentile). That is:

0.901 = 1 - e^(-λx)

e^(-λx) = 0.099

Taking natural logarithm on both sides:

-ln(0.099) = -λx

x = -ln(0.099)/λ

Substituting λ = 1/12,500 = 0.00008:

x = -ln(0.099)/0.00008 ≈ 28,782 hours

Therefore, the answer is B, 28,782 hours.

If the Mean Time Between In-Flight Aircraft Engine Shutdowns Is