Question
Asked Oct 27, 2019
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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.
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Expert Answer

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:

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п x 0,1..,n0 p<l;q=1-p P(X)= (0, otherwise

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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...

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Using the EXCEL formula, BINOM.DIST (6,20,0.20,FALSE) P(X=)0.1091

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