Quick Start Company makes 12-volt car batteries. After many years of product tes

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 45.8 months and a standard deviation of 9.5 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 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? months

Explanation / Answer

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(X < 36) = P(Z < (36 - 45.58)/9.5)

= P(Z < -1.03)

= 0.1515

The company expect to replace 15.15% batteries

b) Let the guarantee be for K months

P(X < K) = 0.1

P(Z < (K - 45.8)/9.5) = 0.1

(K - 45.8)/9.5 = -1.28 (Z value corresponding to 0.1 from standard normal distribution table is -1.28)

K = 33.64

= 34 months

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