4. -/22 pointsBBUnderStat10 5.1.012. USA Today reported that approximately 25% o

Question

4. -/22 pointsBBUnderStat10 5.1.012. USA Today reported that approximately 25% of all state prison inmates released on parole become repeat parole. Suppose the parole board is examining five prisoners up for parole. Let x who become repeat offenders offenders while on 0 number of prisoners out of five on parole 0.206 0.374 0.210-0.192 -0.017 -0.001 (a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) How does this number relate to the probability that none of the parolees will be repeat offenders? O This is twice the probability of no repeat offenders. O These probabilities are not related to each other. O This is five times the probability of no repeat offenders. O These probabilities are the same. O This is the complement of the probability of no repeat offenders. (b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (d) Compute , the expected number of repeat offenders out of five. (Round your answer to three decimal places.)

Explanation / Answer

Let X be the number of prisioners out of 5 on parole who become repeat offenders
a) P(X>=1) = 1 - P(X=0) = 1 - 0.206 = 0.794
Correct Answer: Option (C)
b) P(X>=2) = 1 - P(X=0) - P(X=1) = 1 - 0.206 - 0.374 = 0.42
c) P(X>=4) = P(X=4) + P(X=5) = 0.017 + 0.001 = 0.018
d) Mean = 0(0.206) + 1*0.374 + 2*0.210 + 3*0.192 + 4*0.017 + 5*0.001 = 1.443

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