Suppose X is a normal random variable with mean = 30 and variance =9 (i.e. X~N(30,9) ).

a. What is the probability that X takes the value 30 (i.e., P(X=30))?

b. Find the probability that X falls between 28 and 32.

c. What is P(X>33)?

d. Suppose that all else equal, the variance is now =4. Will the probability computed in b. increase or decrease? Explain.