7.39 Student debt In 2005, a study was conducted in West Texas A&M University. It showed that the average student debt in the United States was $18,367 with a standard deviation of $4709. (Source: http://swer.wtamu.

edu/sites/default/files/Data/15-26-49-178-1-PB.pdf.)

a. Suppose 100 students had been randomly sampled instead of collecting data for all of them. Describe the mean, standard deviation, and shape of the sampling distribution of the sample mean.

b. Using this sampling distribution, find the z-score for a sample mean of $20,000.

c. Using parts a and

b, find the probability that the sample mean would fall within approximately $1000 of the population mean.