Question

After extensive product testing, a battery manufacturer knows that the mean lifetime of its heavy-duty battery is normally distributed with a mean of 45 months and a standard deviation of 10 months. (a) The manufacturer currently guarantees free replacement of any battery that fails within 36 months after purchase. What percentage of the batteries should the manufacturer expect to replace? Show your work. Express probabilities in terms of z scores. (b) If the manufacturer wants to replace 10% or fewer of the batteries under its guarantee policy, for how long should the company guarantee the batteries? (You can round to the nearest month.)

Answer 1