# 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 \$29,625. Assume the population standard deviation is \$6,600 . Suppose that a random sample of 70 USC students will be taken from this population.c. What is the probability that the sample mean will be within \$1,250 of the population mean?.8859How would the probability in part (c) change if the sample size were increased to 150?(to 4 decimals)

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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 \$29,625. Assume the population standard deviation is \$6,600 . Suppose that a random sample of 70 USC students will be taken from this population.

c. What is the probability that the sample mean will be within \$1,250 of the population mean?

.8859

How would the probability in part (c) change if the sample size were increased to 150?

(to 4 decimals)

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Step 1

Solution:

c.

Let X be the cost to attend the university of southern California after deducting grants based on need.

From the given information, n=70, average cost is \$29,625 and population standard deviation is σ=6,600.

Here, the population standard deviation is known. Then, Z test is used test the population mean.

Then, the probability that the sample mean will be within \$1250 of the p...

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