The percentage of “The Room” that a person can watch in a sitting is a random variable with density function

f(x) = 20x3 (1−x) for 0 ≤ x ≤ 100, and zero otherwise. Fifty people are asked to watch the movie.

(a) Estimate the probability that the average amount watched is at least 50%.

(b) Estimate the probability that at least twenty-five people watch at least half the movie.

(c) Explain the difference