According to the Graduate Management Admission Council, the average starting salary for an MBA graduate in the class of 2016 was $105,000. Assume the population standard deviation for starting MBA salaries was $15,000. A random sample of 40 MBA graduates from the class of 2016 was selected.

a. What is the probability that the sample mean is less than $110,000?

b. What is the probability that the sample mean is more than $100,000?

c. What is the probability that the sample mean is between $100,000 and $105,000?

d. Suppose the sample mean was $107,500. Does this result support the findings of Graduate Management Admission Council?