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StatisticsQ&A LibraryAccording 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)Question

Asked Mar 17, 2020

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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)

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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