The number of accidents that occur during a given month at a particular intersection, X, tabulated by a group of Boy Scouts over a long time period is found to have a mean of 12 and a standard deviation of 2. The underlying distribution is not known. What is the probability that, next month, X will be greater than eight but less than sixteen. We thus want P[8

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The number of accidents that occur during a given month at a particular intersection, X, tabulated by a group of Boy Scouts over a long time period is found to have a mean of 12 and a standard deviation of 2. The underlying distribution is not known. What is the probability that, next month, X will be greater than eight but less than sixteen. We thus want P[8 <X<16]. Wecanwrite equation 158 in the following useful manner. P [(µ − kσ) <X<(µ + kµ)] ≥ 1 − 1k2 . For this problem µ = 12 and σ =2soµ− kσ = 12 -2k. We can solve this equation for the k that gives us the desired bounds on the probability

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