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. x 0 1 2 3 4 5 P(x) 0.225 0.364 0.202 0.178 0.030 0.001 (d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.)μ = prisoners(e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)σ = prisoners
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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.
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| P(x) | 0.225 | 0.364 | 0.202 | 0.178 | 0.030 | 0.001 |
μ = prisoners
(e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)
σ = prisoners
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