Assignment:
After deducting grants based on need, the average cost to attend the University of Southern California 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?
Provide complete and step by step solution for the question and show calculations and use formulas.