Exponential and Gamma Distributions

Suppose the mean time to repair a computer has an exponential distribution with mean equal to 2 hours.

a. Find P(repair > 2 hours)

b. P(repair > 4 hours)

c. How much time should be budgeted so that P(repair < budgeted time) ≥ .9?

d. If Y = amount of time, and the repair costs $ = 50 + 100Y + Y2, what are the mean and SD of $?

Five computers from the above problem need repair. Let T be the total time required to repair these five computers.

a. Why does T have a gamma distribution?

b. What are the mean and variance of T?

c. Find P(T > 9) using the Poisson distribution.

d. What would be the normal distribution approximation to P(T > 9)?

e. Why is the normal distribution so inaccurate in this case?