Question

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. x 0 1 2 3 4 5 P(x) 0.227 0.387 0.226 0.122 0.037 0.001 (a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) .773 Correct: Your answer is correct. How does this number relate to the probability that none of the parolees will be repeat offenders? This is twice the probability of no repeat offenders. This is the complement of the probability of no repeat offenders. These probabilities are not related to each other. This is five times the probability of no repeat offenders. These probabilities are the same. Correct: Your answer is correct. (b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) .386 Correct: Your answer is correct. (c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) .038 Correct: Your answer is correct. (d) Compute ?, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) ? = 1.358 Correct: Your answer is correct. prisoners (e) Compute ?, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.) ? = .76 Incorrect: Your answer is incorrect. prisoners

Answer 1

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 repeat offenders?

Answer: This is the complement of the probability of no repeat 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 ?, the expected number of repeat offenders out of five.

e) Compute ?, the standard deviation of the number of repeat offenders out of five.

Answer: First we find the E(X²)

The variance of X is

Therefore the Standard deviation of X is