Question

A battery manufacturer finds that the life of its batteries are normally distributed with a mean of 32 months and a standard deviation of 5 months. Find the probability that a battery lasts more than 36 months. Round off to four decimal places.

Answer 1

Solution:

Given, X follows Normal distribution with,

   = 32

= 5

Find P(a battery lasts more than 36 months)

= P(X > 36)

= P[(X - )/ >  (36 - )/]

= P[Z > (36 - 32)/5]

= P[Z > 0.80]

= 1 - P[Z < 0.80]

= 1 - 0.7881 ( use z table)

= 0.2119

P(a battery lasts more than 36 months) is

0.2119