According to U.S. News & World Report's publication America's Best Colleges, the average cost to attend the University of Southern California (USC) after deducting grants based on need is $27,175. Assume the population standard deviation is $7400. Suppose that a random sample of 60 USC students will be taken from this population.
a. What is the value of the standard error of the mean?
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 $1000 of the population mean?
d. How would the probability in part (c) change if the sample size were increased to 100?