10. Question Details My Notes Ask Your Teacher Quick Start Company makes 12-volt

Question

10. Question Details My Notes Ask Your Teacher 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 9.1 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 a hundredth of a percent.) b) If uick Start does not want to make refunds for more than 14% of its batteres under the full refund guarantee palio guarantee the batteries (to the nearest month)? for o on should he company

Explanation / Answer

Solution:- Given that mean = 45.8, standard deviation = 9.1

a) P(x < 36) = P((x - µ)/? < (36 - 45.8)/9.1)
= P(Z < -1.0769)
= 0.1401
= 14.01%

b) Area to the left = 0.14
Z = -1.08
x = + µ z? = 45.8-1.08*9.1 = 35.972
x = 36 months

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