Poisson Distribution in excel

In summary, the data from www.centralhudsonlab.com showed that the mean number of insect fragments in 225-gram chocolate bars was 14.4, with three brands having contamination more than twice the average. Assuming a Poisson distribution for the number of fragments, the probability of consuming one or more insect fragments in more than one bar is equal to (1 - probability of consuming no insect fragments)^7. For the second question, the probability of a test result being more than twice the mean of 14.4 was calculated to be 0.000463. It is unclear if this can be considered typical variation, as the definition of "typical" is subjective and there is no information on the number of brands tested.
  • #1
27
0

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>
 
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  • #2
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.
 
  • #3
Office_Shredder said:
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.

Thanks for the reply.

Regarding #1, yes, that is what I used, except my (1-P(A does not happen)) is equal to the probability that one is consuming one or more insect fragments in ONE bar. I am just confused on how to apply this to ONE OR MORE bars.

The probability I calculated for #2 is 0.000463. I consider this to be really small, but I really don't understand what is the meaning of typical for this case.
 

What is the Poisson Distribution in excel?

The Poisson Distribution in excel is a statistical function that calculates the probability of a certain number of events occurring within a specific time period. It is used to model the occurrence of rare events, such as accidents or defects, in a given time frame.

How do I use the Poisson Distribution in excel?

To use the Poisson Distribution in excel, you will need to have the Excel Analysis Toolpak installed. Then, type in the formula "=POISSON(x, mean, cumulative)" where x is the number of events you want to calculate the probability for, mean is the average number of events, and cumulative is a logical value that determines whether to calculate the probability of x or less events (TRUE) or exactly x events (FALSE).

What is the difference between Poisson Distribution and Normal Distribution?

Poisson Distribution is used for modeling the probability of rare events occurring in a given time frame, while Normal Distribution is used for modeling continuous data that is symmetrically distributed around a mean value. Additionally, Poisson Distribution deals with discrete data, while Normal Distribution deals with continuous data.

What type of data is suitable for Poisson Distribution in excel?

Poisson Distribution in excel is suitable for discrete data, such as the number of accidents, defects, or events that occur in a given time frame. It is not suitable for continuous data, such as height or weight measurements.

How accurate is the Poisson Distribution in excel?

The accuracy of the Poisson Distribution in excel depends on the quality of the data used and the assumptions made. It is most accurate when the data follows a Poisson distribution and the number of events is relatively small. However, as the number of events increases, the Poisson Distribution tends to approximate the Normal Distribution, which may lead to less accurate results.

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