## Related questions with answers

A safety researcher has found that fourth to sixth graders engaging in unorganized activities on school grounds experienced injuries at the rate of $2.4$ 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

VerifiedFor the Poisson distribution, let us define $x$ as injuries per thousand student-days with a mean of:

$\lambda=2.4/100$

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

$1/\lambda=100/2.4=\boxed{41.67}$

So on the average, there are $41.67$ thousand student-days between injuries.

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