The lifetime of a semiconductor laser at constant power is normally distributed with a mean of 7000 hours and a standard deviation of 600 hours. (a) What proportion of all lasers have lifetimes between 5000 and 8000 hours? (3 MARKS} (1)) Suppose that a failed laser is immediately replaced by a new laser from the same pop- ulation, and assume that replacement lasers are selected randomly and independently. What is the probability that the total lifetime of 5 lasers that are used consecutively will exceed 40000 hours? (4 MARKS} {c} How should the standard deviation of laser lifetimes be changed to ensure that at least 5% all lasers will operate for at least 10000 hours? Write your nal answer as a full sentence. {4 MARKS)