The Food and Drug Administration sets Food Defect Action Levels (FDALs) for some of the various foreign

Question:

The Food and Drug Administration sets Food Defect Action Levels (FDALs) for some of the various foreign substances that inevitably end up in the food we eat and liquids we drink. For example, the FDAL for insect ﬁlth in peanut butter is 3 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A random sample of 50 ten-gram portions of peanut butter is obtained and results in a sample mean of x̄ = 3.6 insect fragments per ten-gram portion.

(a) Why is the sampling distribution of x̄ approximately normal?

(b) What is the mean and standard deviation of the sampling distribution of x̄ assuming that µ = 3 and σ = √3?

(c) What is the probability that a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments? Is this result unusual? What might we conclude?

Distribution
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