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## 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>