# The​ three-year recidivism rate of parolees in a certain state is about20​%;that​ is,20​%of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below.    Find the probability that exactly6out of 20 parolees will end up back in prison within three years. The probability that exactly6out of 20 parolees will end up back in prison isnothing.

Question
69 views
The​ three-year recidivism rate of parolees in a certain state is about
20​%;
that​ is,
20​%
of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below.

Find the probability that exactly
6
out of 20 parolees will end up back in prison within three years.

The probability that exactly
6
out of 20 parolees will end up back in prison is
nothing.
check_circle

Step 1

Solution:

Binomial distribution:

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

Step 2

The probability that exactly 6 out of 20 parolees will end up back in prison within three years is obtained below:

From the given information, the three-year recidivism rate of parolees in a certain state is 0.20, number of parolees is 20. Let...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Other 