Entomologists estimate that an average person consumed almos

Entomologists estimate that an average person consumed almost a pound of bug parts each year. There are that many insect eggs, larvae, and miscellaneous body pieces in the food we eat and the liquids we drink. The Food and Drug Administration (FDA) sets a Food Defect Action Level (FDAL) for each product. For example, the legal limit for peanut butter is 30 insect fragments per 100 grams. You just bought the crackers with 25 grams of peanut butter. What is the probability that the snack will include at least 3 crunchy critters?

A) .0389

B) .9797

C) .2240

D) .9409

Solution

Let X denote the number of insects in 25gms butter.

Given that the level of concentration is 30 fragments per 100 grams of butter = 0.30 fragments per gram.

Here we want to calculate the bug amounts in 25 gms , thus E(X)= 0.30 fragment / g * 25 grams = 7.5 fragments.

Thus, p(X>=3) = 1- p(X<=2)
= 1- ? e^(-7.5) (7.5)^k / k! (k=0 to 2) [ using poisson distribution]

= 1- (0.00055+0.00414+0.01555) = 1-0.02024=0.97976(ans)