Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) (a) P(15 ≤ X ≤ 20) p P(15 ≤ X ≤ 20) P(14.5 ≤ Normal ≤ 20.5) 0.5 0.6 0.8 The normal approximation of P(15 ≤ X ≤ 20) for p = 0.5 is the exact probability of P(15 ≤ X ≤ 20) for p = 0.5. The normal approximation of P(15 ≤ X ≤ 20) for p = 0.6 is the exact probability of P(15 ≤ X ≤ 20) for p = 0.6. The normal approximation of P(15 ≤ X ≤ 20) for p = 0.8 is the exact probability of P(15 ≤ X ≤ 20) for p = 0.8. (b) P(X ≤ 15) p P(X ≤ 15) P(Normal ≤ 15.5) 0.5 0.6 0.8 The normal approximation of P(X ≤ 15) for p = 0.5 is the exact probability of P(X ≤ 15) for p = 0.5. The normal approximation of P(X ≤ 15) for p = 0.6 is the exact probability of P(X ≤ 15) for p = 0.6. The normal approximation of P(X ≤ 15) for p = 0.8 is the exact probability of P(X ≤ 15) for p = 0.8. (c) P(20 ≤ X) p P(20 ≤ X) P(19.5 ≤ Normal) 0.5 0.6 0.8