1) Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of4.8millimeters (mm) and a standard deviation of1.3mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm

(b) the thickness is more than 7.0 mm

(c) the thickness is between 3.0 mm and 7.0 mm

2) 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 of43.2months and a standard deviation of9.5months.

(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 than14%of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

____months

3) A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of91months and a standard deviation of3.5months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.

(a) For how many months should the satellite be insured to be92%confident that it will last beyond the insurance date? (Round your answer to the nearest month.)

____months

(b) If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (Round your answer to four decimal places.)

(c) If the satellite is insured for 84 months, what is the expected loss to the insurance company? (Round your answer to the nearest dollar.)

$____

(d) If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make? (Round your answer to the nearest dollar.)

$____