Question

# Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then...

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. Fifty dash two percent of adults say that they have cheated on a test or exam before. You randomly select six adults. Find the probability that the number of adults who say that they have cheated on a test or exam before is​ (a) exactly four​, ​(b) more than two​, and​ (c) at most five. ​(a) Upper P left parenthesis 4 right parenthesisequals nothing ​(Round to three decimal places as​ needed.) ​(b) Upper P left parenthesis more than two right parenthesisequals nothing ​(Round to three decimal places as​ needed.) ​(c) Upper P left parenthesis at most five right parenthesisequals nothing ​(Round to three decimal places as​ needed.) Which of the events are​ unusual? Select all that apply. A. The event Upper P left parenthesis 4 right parenthesis is unusual. B. The event Upper P left parenthesis more than two right parenthesis is unusual. C. The event Upper P left parenthesis at most five right parenthesis is unusual. D. None of the events are unusual.

Ans:

Use binomial distribution with n=6 and p=0.52

P(x=k)=6Ck*0.52*(1-0.52)6-k

 x P(x) 0 0.0122 1 0.0795 2 0.2153 3 0.3110 4 0.2527 5 0.1095 6 0.0198

a)

P(x=4)=6C4*0.52^4*0.48^2=0.2527

b)

P(x>2)=1-P(x=0)-P(x=1)-P(x=2)

=1-(1-0.52)^6-6C1*0.52*(1-0.52)^5-6C2*0.52^2*(1-0.52)^4

=0.6930

c)

P(at most 5)=P(x<=5)=1-P(x=6)

=1-0.52^6=0.9802

Option D is correct.

None of the events are unusual.

(as all probabilities are greater than 0.05)

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