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 of 53 USC students will be taken from this population. a. What is the value of the standard deviation of the mean? (Note: keep two decimal places.)b. What is the probability that the sample mean will be more than $27,175c. What is the probability that the sample mean will be within $1,000 of population mean? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)d. What would be the probability in Part c if the sample size were increased to 100? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)