1)Power +, Inc

1)Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours. As part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.

(a) What can you say about the shape of the distribution of the sample mean?

The distribution is normal.

(b) What is the standard error of the distribution of the sample mean?

(c) What proportion of the samples will have a mean useful life of more than 36 hours?

(d) What proportion of the sample will have a mean useful life greater than 34.5 hours?

(e) What proportion of the sample will have a mean useful life between 34.5 and 36 hours?

2. Nike’s annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year.

(a) What is the standard error of the mean in this experiment?

(b) What is the probability that the sample mean is between 6 and 7 pairs of sports shoes?

(c) What is the probability that the difference between the sample mean and the population mean is less than 0.25 pair?

(d) What is the likelihood the sample mean is greater than 7 pairs?