Question 1200048: Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 44.0 months and a standard deviation of 8.5 months.
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)
(b) If Quick Start does not want to make refunds for more than 12% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mean is 44 months.
standard deviation is 8.5 months.
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)
17.33%
(b) If Quick Start does not want to make refunds for more than 12% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
34 months
calculator used is at https://davidmlane.com/hyperstat/z_table.html
Answer by ikleyn(52877)  (Show Source):
You can put this solution on YOUR website! .
In the post by @Theo, his picture for the problem (a) is incorrect
(actually, his figure for problem (a), OBVIOUSLY, does relate to problem (b) ).
But the number (the probability 0.1733) is correct, as I checked it.
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