# Poisson Distribution in excel

## Homework Statement

Data from www.centralhudsonlab.com determined
the mean number of insect fragments in 225-gram chocolate
bars was 14.4, but three brands had insect contamination
more than twice the average. Assume
the number of fragments (contaminants) follows a Poisson
distribution.
1)If you consume seven 28.35-gram (one-ounce) bars this
week from a brand at the mean contamination level, what
is the probability that you consume one or more insect
fragments in more than one bar?
2)Is the probability of a test result more than twice the mean
of 14.4 unusual, or can it be considered typical variation?
Explain.

## Homework Equations

Using EXCEL's POISSON.DIST Function.

## The Attempt at a Solution

#1 is really confusing me. I find the wording to be very obscure.
For a poisson distribution we can scale the mean to match the 28.35g bars.
Thus our mean of interest is (28.35/225)*14.4=1.82

My instructor told me that the answer is simply the (probability of consuming one or more insect fragments in ONE bar)^7.
Does this make sense to you guys? Because it doesn't to me.
To me the above is calculating the probability of consuming one or more insect fragments in SEVEN bars, rather than "more than one bar."

#2 seems subjective. More than twice the mean is 28.8. I don't understand what they mean by "typical." Seeing that the problem statement said that 3 brands had contamination more than twice the average, I would assume it's typical, then again it depends on what you define typical as. Any suggestions>

## The Attempt at a Solution

Office_Shredder
Staff Emeritus
Gold Member
For number 1, I would use the fact that P(A happens) = 1-P(A does not happen).

Number 2 is terribly worded. I think they mean something like "find the probability that a tested bar has at least twice as many insect fragments as the mean, and see if that number is really really small". The fact that you don't know how many brands were tested though makes this less than solid logic, but I assume this is what they are going for.

For number 1, I would use the fact that P(A happens) = 1-P(A does not happen).

Number 2 is terribly worded. I think they mean something like "find the probability that a tested bar has at least twice as many insect fragments as the mean, and see if that number is really really small". The fact that you don't know how many brands were tested though makes this less than solid logic, but I assume this is what they are going for.