Problem #8: Data from the Central Hudson Laboratory determined that the mean num

Question

Problem #8: Data from the Central Hudson Laboratory determined that the mean number of insect fragments in 225-gram chocolate bars was 14.4 (http://www.centralhudsonlab.com/chocolates.shtml). In a 35-gram bar the mean number of insect fragments would then be 2.24. Assume that the number of insect fragments follows a Poisson distribution. (a) If you eat a 35-gram chocolate bar, find the probability that you will have eaten at least 2 insect fragments. (b) If you eat a 35-gram chocolate bar every week for 10 weeks, find the probability that you will have eaten no insect fragments in exactly 4 of those weeks. Problem #8(a): Problem #8(b):

Explanation / Answer

Problem 8a:
P(atleast 2 insects) = 1 - P(0 insects) - P(1 insect) = 1 - e-2.24 - e-2.24*2.24 = 0.65507
Formula for P(k events in interval) = e- *(k/k!)

Problem 8b: P(0 insect) = e-2.24,
P(0 insect exactly 4 weeks) = (e-2.24)4 =0.00012845

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