Full-time Ph.D. students receive an average of $12,837 per year. The salaries are normally distributed with a

standard deviation of $5500. If a random sample of 50 students is selected then find the probability that,

a) Sample mean is more than $15,000.

b) In average the student makes between $13,000 and $14,000.

c) Sample mean lies between $11000 and $13500.