USA Today reported that approximately 25% of all state prison inmates released o

Question

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.

(d) Compute , the expected number of repeat offenders out of five. (Round your answer to three decimal places.)

(e) Compute , the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)

x 0 1 2 3 4 5 P(x) 0.219 0.366 0.230 0.151 0.033 0.001

Explanation / Answer

d)

Consider the table:

Thus,          
          
E(x) =mean = Sum(x P(x)) = 1.416   [ANSWER]  

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e)

Var(x) = E(x^2) - E(x)^2 =    1.192944      

s(x) =    1.092219758 [ANSWER, STANDARD DEVIATION]

x (Profit) P(x) x P(x) x^2 P(x) 0 0.219 0 0 1 0.366 0.366 0.366 2 0.23 0.46 0.92 3 0.151 0.453 1.359 4 0.033 0.132 0.528 5 0.001 0.005 0.025

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