Student loan debt is the only form of consumer debt that has grown since the peak of consumer debt in 2008. According to the New York Federal Reserve, the average student loan of somebody younger than 30 is $21,750. Assume the standard deviation for debt is $5,000 per student.

a. What is the probability that the sample mean will be less than $20,000 for a sample size of 30 students?

b. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is $21,750 per student.

c. Answer the question in part a for a sample size of 60. Explain the differences in these two probabilities.