Question

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) P15 s X 20) P P(1S s Xs 20) P(14.5 S Normal s 20.5) 0.5 0.6 0.8 The normal approximation of P(15 s X S 20) for p 0.5 is Select the exact probability of P15 sX S 20) for p- 0.5 The normal approximation of P(15 s XS 20) for p-0.6 is Select Pl 15 x 20) for ρ = 0.6. the exact probability of The normal approximation of p(15寪 Pl 15 s x s 20) for 0.8. 20) for ρ = 0.8 is 41% uxact probability of aem (b) PX s 15) p P(X S 15) P(Normal S 15.5) 0.5 0.6 0.8 The normal approximation of PIX PX 15) for p 0.5. 15) for p 0.5isSelect the exact probability of 15) for ρ = 0.6 is B the exact probability of The normal approximation of p(X P(X 15) for p 0.6. Select The normal approximation of P(x 15) for ρ-0.8 is B the exact probability of select P(X 15) for ρ 0.8. (c) P(20 sX) p P(20 X) P(19.5 Normal) 0.5 0.6 0.8 B the exact probability of The normal approximation of P20 PI20 s X) for p 0.5 X) for ρ " 0.5 iS Select The normal approximation of P(20 sX) for p-0.6 isSelectthe exact probability of PI20 s X) for p 0.6 272019 The normal approximation of Pr20 s x) for p 0.8 isSelectthe exact probability of P120 s X) for p 0.8. You may need to use the appropriate table in the ARRendix of Tables to answer this question.

Answer 1

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