SOLUTION: 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 perso

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Question 376017: 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.
(b) What is the expected number of parolees in Alice's group who will not be repeat offenders? What is the standard deviation?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
let x=.75 and y=.25
(x+y)^4 Binomial distribution.
.
a)
x^4=.3164 P(4)
4x^3y=.4219
6x^2y^2=.2109
4xy^3=.0469
y^4=.0039 P(0)
.
b)
mean=n*p=4*.75=3 the expected number of parolees in Alice's group who will not be repeat offenders.
Standard deviation=sqrt(np(1-p))
=sqrt(4*.75*.25)
=sqrt(.75)
=0.8660
.
Ed