Question

28) 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 7.9 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 9% 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 = = 45.0

standard deviation = = 7.9

a) P(x < 36)

= P[(x - ) / < (36 - 45.0) / 7.9 ]

= P(z < -1.14)

Using z table,

= 0.1271

The percentage is = 12.71%

b) Using standard normal table,

P(Z < z) = 9%

= P(Z < z ) = 0.09

= P(Z < -1.34 ) = 0.09  

z = -1.34

Using z-score formula,

x = z * +

x = -1.34 * 7.9 + 45.0

x = 34.41

x = 34 months