The lifetimes of a certain type of batteries are normally di

The lifetimes of a certain type of batteries are normally distributed with mean value 10 hours and SD 1.5 hours. There are four batteries in a package, and it is reasonable to view them as iid from the population of batteries.

a) Let S be the total lifetime of all four batteries. What is the expected value and variance of S?

b) What is the probability that the total lifetime is greater than 42 hours?

c) Determine the value C for which the total lifetime exceeds C exactly 5% of the time?

Solution