# Poisson Distribution

Could anybody attempt to solve this probability question? It incorporates the Poisson Distribution. Thank You.

A company finds that it issues a mean of 7 pairs of earplugs a week to any employee. What is the probability that the number of pairs taken by any employee is 9 per week? (Using the Poisson Distribution). Explain what the odds are of such overuse.

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Pretty much straightforward question, what have u attempted?

-- AI

Hello Tenali,

Thanks for your response. I cannot find the formula to answer this problem which makes it incresingly difficult to answer.

Poisson Distribution: the probability that n events happend within an interval of length t has a Poisson distribution such that:

P{N(t)=n} = exp(-mt)(mt)^n/n!, for t>=0
where m (often defined as lamda) is the mean rate, i.e., m = 1/mean

For this problem, if we define an event to be a pair of earplug to be issued to an employee, then we are asked to find the probability that exactly 9 pairs of earplugs are taken by any employee a week, thus,
t = 1 week, (note that m and t have the same time units), n = 9
P{N(1)=9}=exp(-1/7*1)(1/7*1)^9/9! = 5.92x10^-14 (apprxo.)