Chapter 6.1, Problem 14P

Criminal Justice: Parole 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. The methods of Section $6.2$ can be used to compute the probability assignments for the r distribution.

x	0	1	2	3	4	5
P(x)	0.237	0.396	0.264	0.088	0.015	0.001

(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 repeal offenders?

(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.

(e) Compute $\sigma$, the standard deviation of the number of repeat offenders out of five.