8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT),...

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8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability th (b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate P(X = 18) exactly and compare to part(b).

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Answer 1

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X N Binomial ( 80106) P=0.6 Given n = 30 We can use central limit theorem for bromial distribution TF min Cop, DPCI-D)) >5 He IS b) PCX=18 by Central limit Theorem 0.14938. c) Now P(x=18) FOT binomial distribution PX=18) n-2 @ $? 44-p) 12 z (30) 0.61

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