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:0.16Step-by-step 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[tex]C = 100 + 60Y + 3Y^2[/tex]C has mean 3124Var(C) = 28,460,160Std dev (C) = [tex]\sqrt{28460160} \\=5334.81[/tex]X = 4000 hoursDifference = [tex]4000-3124 = 876[/tex]Mean diff/std dev = [tex]\frac{876}{5334.81} \\=0.164[/tex]i.e.nearly 0.16  standard deviations above the mean is 4,000 hours