After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175.

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After deducting grants based on need, the average cost to attendthe University of Southern California (USC) is $27,175. Assume thepopulation standard deviation is $7,400. Suppose that a randomsample of 61 USC students will be taken from this population. Whatis the probability that the sample mean will be more than $27,175?What is the probability that the sample mean will be within $1,000of the population mean? (Round your answer to four decimal places.)What is the probability that the sample mean will be within $1,000of the population mean if the sample size were increased to 100?(Round your answer to four decimal places.)