Homes need to be inspected for radon gas which decays and produces alpha particl

Question

Homes need to be inspected for radon gas which decays and produces alpha particles. One device counts the number of alpha particles that hit its detector. To a good approximation, in one area, the count for the next week follows a Poisson distribution with mean 1.3. Determine round your answer to three decimal places) A) the probability of exactly one particle next week B) the probability that of at least two but no more than four particles next week C) the probability that of at least two in the next 2 weeks D) The variance

Explanation / Answer

Sol:

P(X=x)=e^-lmean(mean)^x/x!

P(X=1) =e^-1.3(1.3)/1!

=0.354291

Solutionb:

P(2<X<4)

=P(X=2)+P((X=3)+P(X=4)

=0.2303+0.0998+0.0324

=0.3625

solutionc:

P(X>=2)

=1-P(X=0)+P(X=1)

=1-0.2725-0.354291

=0.3732

sOLUTIONd

variancde=mean for poisson distribution'

variance=1.3

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