After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $25,525. Assume the population standard deviation is $6,800. Suppose that a random sample of 50 USC students will be taken from this population. Use z-table. a. What is the value of the standard error of the mean? (to nearest whole number) b. What is the probability that the sample mean will be more than $25,525? (to 2 decimals) c. What is the probability that the sample mean will be within $1,000 of the population mean? (to 4 decimals) d. How would the probability in part (c) change if the sample size were increased to 180 ? (to 4 decimals)