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.

x	0	1	2	3	4	5
P(x)	0.230	0.374	0.227	0.141	0.027	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?

These probabilities are not related to each other.These probabilities are the same.     This is twice the probability of no repeat offenders.This is five times the probability of no repeat offenders.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 μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.)
μ =  prisoners

(e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)
σ =  prisoners

Answer 1

a) The probability that one or more of the five parolees will be repeat offenders is computed here as:

P(X >=1) = 1 - P(X = 0) = 1 - 0.230 = 0.770

Therefore 0.770 is the required probability here.

Now the probability that none of the parolees will be repeat offenders is computed here as:

P( X = 0) = 1 - P(X >=1)

Therefore This is the complement of the probability of no repeat offenders.

b) The required probability here is computed as:

P(X >=2 ) = 1 - P(X = 0) - P(X = 1) = 1 - 0.230 - 0.374 = 0.396

Therefore 0.396 is the required probability here.

c) The required probability here is computed as:

P(X >= 4) = P(X = 4) + P(X = 5) = 0.027 + 0.001 = 0.028

Therefore 0.028 is the required probability here.

d) Now the expected number of repeat offenders out of five is computed here as:

Therefore 1.364 is the mean number required here.

e) The second moment is first computed as:

Therefore the standard deviation is now computed here as:

Therefore 1.07 is the required standard deviation here.