In: Statistics and Probability
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) | 0.200 | 0.376 | 0.230 | 0.152 | 0.041 | 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.)
How does this number relate to the probability that none of the
parolees will be repeat offenders?
These probabilities are not related to each other.This is twice the probability of no repeat offenders. This is five times the probability of no repeat offenders.These probabilities are the same.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. (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.)
(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
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 2034 raffle tickets at $5 per ticket.
(a) Kevin bought nineteen 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 nineteen
tickets?
---Select--- more less
How much did Kevin effectively contribute to the Samaritan Center
for the Homeless? (Round your answer to two decimal places.)
$