Question

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.)

P(0) =

P(1) =

P(2) =

P(3) =

P(4) =

(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.)

(d) How large a group should Alice counsel to be about 98% sure that three or more parolees will not become repeat offenders?

Answer 1

Probability that a person does not become a repeat offender,

p = 1 - 0.25 = 0.75

n = 4

(a)

P(0) = = 0.004

P(1) = = 0.047

P(2) = = 0.211

P(3) = = 0.422

P(4) = = 0.316

(c)

Expected number of parolees in Alice's group who will not be repeat offenders = = 3

Standard deviation = = 0.866 ≈ 0.87

(d)

Let n be the size of the group

Thu, Mean number of parolees who will not become repeat offenders

= 0.75n

Standard deviation of parolees who will not become repeat offenders

=

The required condition is that P(X ≥ 3) ≈ 0.98

Using correction of continuity, P(X ≥ 3) ≈ P(X > 2.5) ≈ 0.98

Corresponding z value = -2.054

->

-> n ≈ 6.3

Thus, Alice should counsel a group of 7 people