Question

# 1. USA Today reported that approximately 25% of all state prison inmates released on parole become...

1. 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) 0.223 0.375 0.217 0.153 0.031 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.)

(b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

(c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)
Ans= 0.032

(d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.)
μ =   prisoners

(e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)
σ =   prisoners

2.  The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at \$2000. The students sold 2663 raffle tickets at \$5 per ticket.

(a) Kevin bought twenty-seven tickets. What is the probability that Kevin will win the spring break cruise to the Caribbean? (Round your answer to five decimal places.)

What is the probability that Kevin will not win the cruise? (Round your answer to five decimal places.)

(b) Expected earnings can be found by multiplying the value of the cruise by the probability that Kevin will win. What are Kevin's expected earnings? (Round your answer to two decimal places.)
\$

Is this more or less than the amount Kevin paid for the twenty-seven tickets?

How much did Kevin effectively contriute to the Samaritan Center for the Homeless? (Round your answer to two decimal places.)
\$

3. Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 49% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.

(a) Out of five adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(b) Out of five adults, all are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(c) Out of five adults, exactly three are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

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