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 43.2 months and a standard deviation of 6.7 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 12% 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

Solution :

Given that ,

mean = = 43. 2

standard deviation = = 6.7

P(x <36 ) = P[(x - ) / < (36 - 43.2) /6.7 ]

=P (Z <-1.07)

=0.1423

answer = 14.23%

Using standard normal table,

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12

= P(Z < z ) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z <1.18 ) = 0.88

z = 1.18

Using z-score formula  

x = z +

x =1.18 *6.7+43.2

x = 51. 106

x=51

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