Question

The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? (Round your answer to two decimal places.)

Answer 1

Let denotes the life time of i th battery.

Here,

Let S denotes the total lifetime of all 4 batteries in a package, i.e.

We can write,

or

Now, to find s such that

(ans)