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
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?
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>