4. Each of 3 friends bring one flashlight containing a fresh battery for their camping trip, and they decide to use one flashlight at a time. Let X1, X2, and X3 denote the lives of the batteries in each of the 3 flashlights, respectively.

Suppose that they are independent normal random variables with expected values μ1 = 6, μ2 = 7, and μ3 = 8 hours, and variances σ2 1 = 2, σ2 2 = 3, and σ2 3 = 4, respectively.

(a) Find the 95th percentile of the total duration of the flashlights.

(b) Calculate the probability that the flashlights will last a total of less than 25 hours.

(c) Suppose that the 3 friends have five camping trips that year and each time they start with the same types of fresh batteries as above. Find the probability that the batteries last more than 25 hours exactly 3 of the 5 times.