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 46.2 months and a standard deviation of 7.3 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.) 1 Incorrect: Your answer is incorrect. % (b) If Quick Start does not want to make refunds for more than 7% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

Answer 1

Solution :

Given that ,

mean = = 46.2

standard deviation = = 7.3

a) P(x < 36)

= P[(x - ) / < (36 - 46.2) / 7.3 ]

= P(z < -1.40)

Using z table,

= 0.0808

The percentage is = 8.08%

b) Using standard normal table,

P(Z < z) = 7%

= P(Z < z ) = 0.07

= P(Z < -1.48 ) = 0.07  

z = -1.48

Using z-score formula,

x = z * +

x = -1.48 * 7.3 + 46.2

x = 35.40

x = 35 months