Question

The length of time Y necessary to complete a key operation in the construction of houses has an exponential distribution with mean 18 hours. The formula C = 100 + 60Y + 3Y2 relates the cost C of completing this operation to the square of the time to completion. The mean of C was found to be found to be 3,124 hours and the variance of C was found to be 28,460,160. How many standard deviations above the mean is 4,000 hours? (Round your answer to two decimal places.)

Answer 1

0.16

Explanation:

Given that the length of time Y necessary to complete a key operation in the construction of houses has an exponential distribution with mean 18 hours.

The formula for cost of completing this operation is

`C = 100 + 60Y + 3Y^2`

C has mean 3124

Var(C) = 28,460,160

Std dev (C) =
`√(28460160) \\=5334.81`

X = 4000 hours

Difference =
`4000-3124 = 876`

Mean diff/std dev =
`(876)/(5334.81) \\=0.164`

i.e.nearly 0.16 standard deviations above the mean is 4,000 hours