Question

A government entity sets a Food Defect Action Level​ (FDAL) for the various foreign substances that inevitably end up in the foods we eat. The FDAL level for insect filth in peanut butter is

0.20.insect fragment​ (larvae, eggs, body​ parts, and so​ on) per gram. Suppose that a supply of peanut butter contains 0.20.insect fragment per gram. Compute the probability that the number of insect fragments in a 6​-gram sample of peanut butter is ​(a) exactly two. Interpret the results.​(b) fewer than two. Interpret the results.​(c) at least two. Interpret the results.​(d) at least one. Interpret the results.​(e) Would it be unusual for a 6​-gram sample of this supply of peanut butter to contain four or more insect​ fragments?

Answer 1

Let X denotes the number of insect fragments in a 6​-gram sample of peanut butter.

X ~ Binomial(n = 6, p = 0.2)

The probability mass function of X is

Now,

a) The probability that the number of insect fragments in a 6​-gram sample of peanut butter is exactly two

b) The probability that the number of insect fragments in a 6​-gram sample of peanut butter is fewer than two

c) The probability that the number of insect fragments in a 6​-gram sample of peanut butter is at least two

d) The probability that the number of insect fragments in a 6​-gram sample of peanut butter is at least one

e) The probability that the number of insect fragments in a 6​-gram sample of peanut butter is at least four

Since P(X>=4) < 0.05, so we can say that for a 6​-gram sample of this supply of peanut butter to contain four or more insect​ fragments would be unusual.