11127 points I Previous Anewers DevoreStar 4.E.053 Let X have a binomial distrib
ID: 3040085 • Letter: 1
Question
11127 points I Previous Anewers DevoreStar 4.E.053 Let X have a binomial distribution with parameters n = 25 and P Calculate each of the following probabilities using the normal approximation with he 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 bx n, p). (Round your answers to four decimal places.) (a) Pi15 s Xs 20) p P15 X20) P(14.5 Normal 20.5) 0.5 2110 0.6 5800 0.8 0.0007 2112 070 5963 The normal approximation of 15s X s 20) for p-0.5 is! less than the exact probability of 15 s x s 20) for p-0.5. The normal approximation of P(15s X 20) for p = 0.5 is Less than the exact probability of 15 SX s20) for 06. The normal approximation of Pl 15 s X2 20) for P = 0.3 is greater than -thexact probability of P(15 s X2 20) for P = 0.8. (b) PX 15) P PXS 15) P(Normal S 15.5) 0.5 577 0.6 0.8 1222 The normal approximation of P(X2 15) for P 0.5 is less than The normal approximation of 15) for p-o.6 is greater than The normal approximation of P(Xs 15) for p-0.3 is | less than the exact probability of P(Xs 15) for: 0.5. the exact probability of P(X s 15) for p-0.6. the exact probability of P(Xs 15) for p-0.3. (c) Pi20 s x) p P(20 X) P19.5 Normal) 0.5 0.6 0.8 0.0207 The normal approximation of 20 s X) for p-0.5 islgresterthanM v' the exact probability of P(20 s X) for p-0.5. The normal approximation of 20 s x) for = 0.6 is realer than -the exact probability of P(20 S X) for 06. The normal approximation of P(20 X) for P 0.8 is less than -the exact probability of P120 X) for: 0.3. You may nead to use the appropriate tabla in the Appendix of Tables to answar this quastion.Explanation / Answer
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b)
c)
P(15<=X<=20) P(14.5<X<20.5) 0.2117 0.2112 0.5763 0.5685 0.5738 0.5957Related Questions
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