USA Today reported that approximately 25% of all state prison inmates released o
ID: 3267116 • Letter: U
Question
USA Today reported that approximately 25% of all state prison inmates 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 repeat offenders. (a) Find the probability that one or more of the five parolees will be repeat offenders. How does this number relate to the probability that none of the parolees will be repeat offenders? This is five times the probability of no repeat offenders. This is the complement of the probability of no repeat offenders. This is twice the probability of no repeat offenders. These probabilities are not related to each other. These probabilities are the same. (b) Find the probability that two or more of the five parolees will be repeat offenders. (c) Find the probability that four or more of the five parolees will be repeat offenders. (d) Compute mu, the expected number of repeat offenders out of five. mu = prisoners (e) Compute sigma, the standard deviation of the number of repeat offenders out of five. sigma = prisonersExplanation / Answer
Solution:-
a) 0ne or more = 1 - 0.212 = 0.788
==> option B. this is the complement of the probability of no repeat offenders.
b) 0.228+0.148+0.045+0.001 = 0.422
c) 0.045+0.001 = 0.046
d) = (n p) = 1.25 prisoners
e) = ( n p q ) = 0.97 prisoners
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