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 45.4 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.)
%

(b) If Quick Start does not want to make refunds for more than 13% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
months

Attendance at large exhibition shows in Denver averages about 8080 people per day, with standard deviation of about 475. Assume that the daily attendance figures follow a normal distribution. (Round your answers to 4 decimal places.)

(a) What is the probability that the daily attendance will be fewer than 7200 people?


(b) What is the probability that the daily attendance will be more than 8900 people?


(c) What is the probability that the daily attendance will be between 7200 and 8900 people?

Suppose you want to eat lunch at a popular restaurant. The restaurant does not take reservations, so there is usually a waiting time before you can be seated. Let x represent the length of time waiting to be seated. From past experience, you know that the mean waiting time is μ = 18.8 minutes with σ = 4.4 minutes. You assume that the x distribution is approximately normal. (Round your answers to four decimal places.)

(a) What is the probability that the waiting time will exceed 20 minutes, given that it has exceeded 15 minutes? Hint: Compute P(x > 20|x > 15).


(b) What is the probability that the waiting time will exceed 25 minutes, given that it has exceeded 18 minutes? Hint: Compute P(x > 25|x > 18).

Answer 1