IEEE Transactions (June 1990) presented a hybrid algorithm for solving polynomial 0–1 mathematical programming problems. The solution time (in seconds) for a randomly selected problem solved using the hybrid algorithm has a normal probability distribution with mean μ = .8 second and σ = 1.5 seconds. Consider a random sample of n = 30 problems solved with the hybrid algorithm.

a. Describe the sampling distribution of S², the variance of the solution times for the 30 problems.

b. Find the approximate probability that S² will exceed 3.30.