The following problems are designed to give you practice calculating z scores and using them to solve problems..... I recommend that you review the synopsis information on the normal distribution, prior to completing them. It also contains a normal curve applet, which will be useful in solving the problems: Synopsis: Normal Distribution and Central Limit Theorem.
According to U.S. News & World Report data, in 1995 tuition costs at Indiana University, a public university, were $2,984 per year, while the tuition costs at the University of Evansville, a private university in Indiana, were $11,800 per year. In that same year the average cost of tuition at all public U.S. colleges was $2,208, with a standard deviation of $1,041, and the average cost of tuition at all private U.S. colleges was $10,979.68, with a standard deviation of $4,057.
a. What is the z score for Indiana University?
b. What is the z score for the University of Evansville?
c. Which school was more expensive to attend in 1995, relative to the cost of education in its own category?
d. What is the probability of a private university costing less than $11,800? (Hint: Use the mean and standard deviation values for all private schools to answer this question.)
e. What is the probability of a public university costing less than $2,984? (Hint: Use the mean and standard deviation values for all public schools to answer this question.)