Question

A safety researcher has found that fourth to sixth graders engaging in unorganized activities on school grounds experienced injuries at the rate of 2.42.4 injuries per 100 thousand student-days. On the average, how many student-days elapse between injuries to fourth to sixth graders in unorganized activities at school, and what is the probability that the next such injury will occur before 45 thousand student-days have passed?

Solution

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Answered 11 months ago
Answered 11 months ago
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For the Poisson distribution, let us define xx as injuries per thousand student-days with a mean of:

λ=2.4/100\lambda=2.4/100

Let us redefine xx in the exponential distribution. Note that the mean of the corresponding exponential distribution is equal to 1/λ1/\lambda and is the inverse of the mean of the Poisson distribution such that:

1/λ=100/2.4=41.671/\lambda=100/2.4=\boxed{41.67}

So on the average, there are 41.6741.67 thousand student-days between injuries.

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