USA Today reports that about 25 of all prison parolees becom

USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.

(a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)

(b) Make a histogram for the probability distribution of part (a).

(c) What is the expected number of parolees in Alice\'s group who will not be repeat offenders? (Round your answer to two decimal places.)
parolees

What is the standard deviation? (Round your answer to two decimal places.)
parolees

Solution

P(r) = Probability that r out of 4 will not reoffend

Let p = probability a parolee will not reoffend = 0.75
1-p = probability a parolee will reoffend = 1-0.75 = 0.25

P(r) = 4Cr * p^r * (1-p)^(4-r)

P(0) = 4C0 * 0.75? * 0.25? = 0.00390625 . = 0.004
P(1) = 4C1 * 0.75