Generation Y has been defined as those individuals who were born between 1981 and 1991. According to the ­Project on Student Debt, Generation Y students graduating from college averaged $ 23,200 in debt. Assume the standard deviation for debt is $ 7,500 per student.

a. What is the probability that the sample mean will be less than $ 24,000 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 $ 23,200 per student.

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