please help need to understand how to work these 3, USA Today reported that appr

Question

please help need to understand how to work these

3, USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offanders while on parole. Suppose the parole board is examining five prisoners up for parole?Let x : number of prisoners out of five parole who become repeat offandars, and their corresponding probabilities. P) 0.237 0.369 0264 0.088 0.015 0.001 What is the probability that one or more of the five parolees will be repeat offenders? How does this number relate to the probability that none of the parolees will be repeat offenders? a. b. Find the probability that two or more of the five parolees will be repeat offenders c. Find the probability that two or less of the five parolees will be repeat offenders d. Compute the mean number of repeat offenders out of five. e. Compute the standard deviation of the number of repeat offenders out of five.

Explanation / Answer

Ans:

It is binomial distribution with n=5,p=0.25

a)P(one or more)=P(x>=1)=1-P(x=0)=1-P(none)=1-0.237=0.763

b)P(x>=2)=1-P(x=0)-P(x=1)=1-0.237-0.396=0.367

c)P(x<=2)=P(x=0)+P(x=1)+P(x=2)=0.237+0.396+0.264=0.896

d)mean=np=5*0.25=1.25

e)standard deviation=sqrt(np(1-p))=sqrt(5*0.25*(1-0.25))=0.968

(in above table mean and standard deviation is calculated using discrete prob. formulas,it will be same using binomial mean and std dev formulas)

x p(x) x*p(x) (x-1.25)^2*p(x) 0 0.237 0 0.371 1 0.396 0.396 0.025 2 0.264 0.527 0.148 3 0.088 0.264 0.269 4 0.015 0.059 0.111 5 0.001 0.005 0.014 Total 1.000 1.25 0.938 variance mean 0.968 std dev

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