Data from the Central Hudson Laboratory determined that the mean number of insec
ID: 3202347 • Letter: D
Question
Data from the Central Hudson Laboratory determined that the mean number of insect fragments in 225-gram chocolate bars was 14.4. In a 32-gram bar the mean number of insect fragments would then be 2.05. Assume that the number of insect fragments follows a Poisson distribution. If you eat a 32-gram chocolate bar, find the probability that you will have eaten at least 2 insect fragments. If you eat a 32-gram chocolate bar every week for 9 weeks, find the probability that you will have eaten no insect fragments in exactly 6 of those weeks.Explanation / Answer
(a)
In a 32 gram bar the mean number of insect fragments would then 2.05.
Here we need to find P (x 2)
P (x 2) = 1 – P (x < 2)
= 1 – [P (x = 0 ) + P ( x= 1 )]
P (x) = [ (e^-m * m^x) / x! ] [Poisson distribution]
Mean (m ) = 2.05
p (x = 0) = [ (e^-2.05 * 2.05^0) / 0! ]
= 0.1287
p (x = 1) = [ (e^-2.05 * 2.05^1) / 1! ]
= 0.2639
P (x 2) = 1 – P (x < 2)
= 1 – [P (x = 0 ) + P ( x= 1 )]
= 1 – [ 0.1287 + 0.2639 ]
= 1 – 0.3926
= 0.6074
Answer: 0.6074
(b)
Mean (m) = 2.05 *9
= 18.45
P ( x = 6 ) = [ (e^-18.45 * 18.45^6) / 6! ]
= 0.0005
Answer: 0.0005
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