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 45.0 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 6% 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

we have given mean (u) = 45

standard deviation () = 8.7

a ) P(x< 36) = P (z <)

= P (Z<−1.03)=0.1515

15.15% of its batteries will the company expect to replace.

b ) from z table we came to know that

P(z =-1.55) = 0.06

x = -1.55*8.7 +45

x = 45-13.485

x = 31. 515 = 32 month approx

32 month approx should the company guarantee the batteries