After deducting grants based on need, the average cost to attend the University

Question

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175 (U.S. News & World Report, America’s Best Colleges, 2009 ed.). Assume the population standard deviation is $7,400. Suppose that a random sample of 60 USC students will be taken from this population.

a. Refer to Exhibit 2. What is the value of the standard deviation of the mean? (Note: keep two decimal places.)

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 $1,000 of population mean? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)

d.What would be the probability in Part c if the sample size were increased to 100? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)

Explanation / Answer

a) std deviation of the mean =population std deviation/sqrt(n)=7400/sqrt(60)=955.34

b )as z score=(X-mean)/std deviaiton

P(Xbar>27175)=P(Z>(27175-27175)/955.34)=P(Z>0)=0.000

c)probability that the sample mean will be within $1,000 of population mean

=P(-1000/955.34<Z<1000/955.34)=P(-1.05<Z<1.05)=0.8531-0.1469=0.7062

d) std deviation of the mean =population std deviation/sqrt(n)=7400/sqrt(100)=740

probability that the sample mean will be within $1,000 of population mean

=P(-1000/740<Z<1000/740)=P(-1.35<Z<1.35)=0.9115-0.0885=0.8230

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.