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 44.4 months and a standard deviation of 7.7 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.)

13.79% of the batteries will Quick Start Company expect to replace on any battery that fails within a 36-month period after purchase.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean of the average life of a Quick Start battery = 44.4 months

Standard deviation of the average life of a Quick Start battery = 7.7 months

2. 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?

For finding the percentage of batteries will Quick Start Company expect to replace within a 36-month period, we make this calculations:

1. Find the z-score for 36 months:

z-score = 36 - 44.4/7.7 = - 8.4/7.7 = - 1.09

2. Now, find p for z-score = - 1.09, using a z-score table:

p = 0.1379

13.79% of the batteries will Quick Start Company expect to replace on any battery that fails within a 36-month period after purchase.