A certain company makes 12volt car batteries After many year

A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed with a mean of 56 months and a standard deviation of 6 months. If the company does not want to make refunds for more than 10% of its batteries under a full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

Solution

let y be warranty months

X be number of months the battery runs

X follows Normal distribtuion with mean = 56 and sd = 6

Now, P(X < y) = 0.1

=> P(Z < (y - 56)/6 ) = 0.1

From the standard normal table, Z = -1.282

=> (y - 56)/6 = -1.282

=> y = 48.308

Therefore, Number of Warranty months = 48