Question

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 8.7 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 13% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? months

Answer 1

Let "X" be Quick Start guarantees a full refund on any battery that fails.

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-0.92, TRUE)" to find the probability.

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Refer Z-table, Lookup for Z-value corresponding to area 0.13 to the left of the normal curve or use excel formula "=NORM.S.INV(0.13)" to find the Z-value.