Suppose a radioactive source is metered for two hours, during which time the tot

Question

Suppose a radioactive source is metered for two hours, during which time the total number of alpha particles counted is 482. What is the probability that exactly three particles will be counted in the next two minutes? Answer the questions two ways - first, be defining X to be the number of particles counted in two minutes, and second, by defining X to be the number of particles counted in one minute.

Explanation / Answer

Average(?)=482 alpha particles/ 2 hours = 241?/hr x (1hr/60 min) => ?=4.0167?/min We want the average number of ?-particles in 2 minutes, hence 4.0167?/min x 2 min = 8.033 ? particles By the Poisson distribution: P(X=3)=[(8.033)^3 x e^-(8.033)] / 3! => P(X=3)=0.028

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