Chapter 7 and 8 Lab

MAT 152

Name:__________________________

For all problems, in addition to answering the question, use probability notation to describe the problem and draw and appropriately label a normal probability distribution curve to model the problem. 3 points per question.

1. The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be

a. Less than

b. Longer than 5 minutes?

c. Between 8 and 15 minutes?

2. Blood type AB is found in 3% of the population. If 350 people are chosen at random,

a. Describe the sampling distribution of the sample proportion.

b. What is the probability that 10 or more will have this blood type.

c. Between 10 and 20 will have this blood type?

3. One environmental group did a study of recycling habits in a California community. It found that 70% of the aluminum cans sold in the area were recycled.

a. Describe the sampling distribution of the sample proportion. (n = 400)

b. If 400 cans are sold today, what is the probability that 300 or more will be recycled?

c. Of the 400 can sold, what is the probability that between 260 and 300 will be recycled?

4. Future Electronics makes compact disk players. Its research department found that the life of the laser beam device is normally distributed, with mean 5000 hours and standard deviation 450 hours.

a. Find the probability that the laser beam device will wear out in 4300 hours or less.

b. Future Electronics wants to place a guarantee on the players so that no more than 5% fail during the guarantee period. Because the laser pickup is the part likely to wear out first, the guarantee will be based on the life of the laser beam device. How many hours should the guarantee cover? (round to the next playing hour)

5. A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with a mean of 38 minutes and a standard deviation of 5 minutes.

a. The drug is administered to a patient at random, what is the probability that the time it takes to go into effect is 35 minutes or less?

b. The drug is administered to a random sample of 10 patients.

Describe the sampling distribution of the sample mean.

c. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less?

c. Comment on the differences of the results in part a and part b.

6. Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 75 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with a mean of 75 tons and a standard deviation of 0.8 tons.

a. What is the probability that one car chosen at random will have less than 74.5 tons of coal?

b. What is the probability that a sample of 20 cars chosen at random will have a mean load weight of less than 74.5 tons of coal?

c. Suppose the weight of coal in one car was less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Suppose the weight of coal in 20 cars selected at

random had an average of less than 74.5 tons? Would that fact make you suspect the loader had slipped out of adjustment? Why?

7. Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 months and the distribution is normal.

a. If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production should the company expect to replace?

b. If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)?

8. Find z such that 5% of the area under the standard normal curve lies to the right of z.

9. Find z such that 99% of the area under the standard normal curve lies between -z and z.

10. Express Courier Service has found that the delivery time for packages is normally distributed with mean 14 hours and standard deviation 2 hours.

a. For a package selected at random, what is the probability that it will be delivered in 18 hours or less?

b. What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time?