Problem 3.41 The random variable X has the binomial distribution B(x; n, p). Compute the following probabilities using the binomial tables.

(a) P(X ≤ 4) = B(4; 10, p) for p = 0.1, 0.4, 0.6, 0.8

(b) P(X > 9) = 1 − B(9; 20, p) for p = 0.2, 0.5, 0.7, 0.9 Problem 3.42 For n = 20 and p = 0.5

(a) Estimate P(|X − 10| ≥ 5) using Chebyshev’s inequality.

(b) Compute P(|X − 10| ≥ 5) using the binomial tables. Problem 3.43 Show that b(x; n, p) = b(n − x; n, 1 − p) and give an intuitive explanation for this identity. Problem 3.44

(a) Compute b(x; 15, 0.3) for x = 0, 1, 2, 3 directly using Equation 3.33.

(b) Compute b(x; 15, 0.3) for x = 0, 1, 2, 3 using the recurrence Equation 3.36. Problem 3.45 A multiple choice quiz has 10 questions each with four alternatives. A passing score is 6 or more correct. If a student attempts to guess the correct answer to each question what is the probability that he passes?