21) Suppose 30% of UI students smoke. If 10 UI students are selected randomly, w

Question

21) Suppose 30% of UI students smoke. If 10 UI students are selected randomly, what is the probability that exactly 4 of them smoke. a) .08 b) 10c) 14d) 16) 20 22) Continuing problem (21), find the probability that fewer than 3 of the selected students smoke a) 383 b) 412 c) 432) 464e) 488 It was reported in Campus Review (June, 2015) that 32% of college students in the US work more than 20 hours per week. Find the probability that exactly four of ten randomly chosen US college students work more than 20 hours per week. 23) a) 084 b) 125 c) .164 d) .200 e) 218 30% of the pencils used Co., the rest were produced by GlaxCo, 5% of Acme pencils are defective, whereas 2% of GlaxCo pencils are defective. Find the probability that a pencil was produced by Acme, given that it is defective a) .500 b) .517 c).532 d) .544 e) .565 24) your office were produced by Acme Pencil

Explanation / Answer

Ans:

21)Use binomial distribution with n=10 and p=0.3

P(exactly 4)=P(x=4)=10C4*0.34*(1-0.3)6=0.20

option e is correct(0.20)

22)

P(x<3)=P(x<=2)=P(x=0)+P(x=1)+P(x=2)

=10C0*0.30*(1-0.3)10+10C1*0.31*(1-0.3)9+10C2*0.32*(1-0.3)8

=0.028+0.121+0.233

=0.383

Option a is correct(0.383)

23)Use binomial distribution with n=10 and p=0.32

P(exactly 4)=P(x=4)=10C4*0.324*(1-0.32)6=0.218

option e is correct(0.218)

24)

P(Acme)=0.3

P(GlaxoCo.)=0.7

P(defective/Acme)=0.05

P(defective/Glaxoco.)=0.02

P(defective)=P(defective/Acme)*P(Acme)+P(defective/Glaxoco)*P(Glaxoco)

=0.05*0.30+0.02*0.70

=0.029

P(Acme/defective)=P(defective/Acme)*P(Acme)/P(defective)

=0.05*0.30/0.029

=0.517

Option b is correct(0.517)

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