You may need to use the appropriateappendix tableortechnologyto answer this question.

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7,400. Suppose that a random sample of54USC studentswill be taken from this population.

(a)

What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)

$

(b)

What is the probability that the sample mean will be more than $27,175?

(c)

What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)

(d)

What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)