Question

You may need to use the appropriate appendix table or technology to answer this question. A binomial probability distribution has p = 0.20 and n = 100. (a) What are the mean and standard deviation? mean standard deviation (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. No, because np > 5 and n(1 - p) > 5. Yes, because n > 30. No, because np < 5 and n(1-p) < 5. Yes, because np < 5 and n(1 - p) < 5. Yes, because np > 5 and n(1-P) 2 5. (c) What is the probability of exactly 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) (d) What is the probability of 16 to 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) (e) What is the probability of 12 or fewer successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

Answer 1

P2o.2 n=100 a) mean ang 100 x0220 bo standard deviation a ſupa Toox0.9X08 b) np : 100X0.2 = 20 5 1 loor 6: 6 - Bo 25 option e is correct () P(x=24) (By using connnung correction) P(23-5 < X<24.5) :P ( 25.9 -20 < 24 2015-20) 27 Mate] -P (0984241.13) = P(221:13) - P(220.88) 1 0-8708 - 0-0106 0.060L [P-value from 2-table] d) P1163 X320) p(15.5<x<24,5) :p ( 15.052017 24.5.20) P(-1.13224 0.88) P120.98) - P(26-1-13) = 0.8106 - 0.1292 0.6814 c) P(x512)=P(x < 12.5) =p(22125720 =P(22-188) 0.03005