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Social ScienceThe 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.
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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
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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