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

Question 974111: 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.)

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 by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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) = 4C0*(0.75)^0*0.25^4
P(1) = 4C1*(0.75)*0.25^3
P(2) = 4C2*(0.75)^2 * 0.25^2
P(3) = etc.
P(4) = etc.
(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.)
Ans: mean = np = 4*0.75 = 3
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What is the standard deviation? (Round your answer to two decimal places.)
Ans: std = sqrt[npq] = sqrt[3*0.25] = (1/2)sqrt(3)
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(d) How large a group should Alice counsel to be about 98% sure that three or more parolees will not become repeat offenders?
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Cheers,
Stan H.
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