USA Today reported that approximately 25% of all state prison inmates released on parole become repeat...

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USA Today reported that approximately 25% of all state prisoninmates released on parole become repeat offenders while on parole.Suppose the parole board is examining five prisoners up for parole.Let x = number of prisoners out of five on parole who become repeatoffenders.
x 0 1 2 3 4 5 P(x) 0.216 0.360 0.226 0.162 0.035 0.001
(a) Find the probability that one or more of the five parolees willbe repeat offenders. (Round your answer to three decimal places.)How does this number relate to the probability that none of theparolees will be repeat offenders? These probabilities are thesame. This is twice the probability of no repeat offenders. This isfive times the probability of no repeat offenders. This is thecomplement of the probability of no repeat offenders. Theseprobabilities are not related to each other. Correct: Your answeris correct.
(b) Find the probability that two or more of the five parolees willbe repeat offenders. (Round your answer to three decimalplaces.)
(c) Find the probability that four or more of the five paroleeswill be repeat offenders. (Round your answer to three decimalplaces.)
(d) Compute Î¼, the expected number of repeat offenders out of five.(Round your answer to three decimal places.) Î¼ = prisoners
(e) Compute Ïƒ, the standard deviation of the number of repeatoffenders out of five. (Round your answer to two decimal places.) Ïƒ= prisoners

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3.7 Ratings (531 Votes)

x 0 1 2 3 4 5

P(x) 0.206 0.360 0.226 0.162 0.035 0.001

a)probability that one or more of the five parolees will be repeat offenders=1-probability that less than one of the five parolees will be repeat offender =1-probability that less than one of the five parolees will be repeat offender =

=1-0.206 =0.794

b)probability that two or more of the five parolees will be repeat offenders=1-robability that one or less than one of the five parolees will be repeat offenders=1-P(0)-P(1) =1-(0.206+0.360)=0.434

c)probability that four or more of the five parolees will be repeat offenders=P(4)+P(5)=0.035+0.001=0.036

d)expected no offfenders=0*(0.206)+1*(0.360)+2(0.226)+3*(0.162)+4*(0.035)+5*(0.001)=1.443

e)variance=(0-1.443)^2*(0.206)+(1-1.443)^2*(0.360)+(2-1.443)^2*(0.226)+(3-1.443)^2*(0.162)+(4-1.443)^2*(0.035)+(5-1.443)^2*(0.001)
=0.4289 + 0.0706 +0.0701+0.4142 +0.2288+0.0035 =1.22

standard deviation=sqrt(1.22)=1.10

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