Data from www.centralhudsonlabs.com determined the mean number of insect fragments in 225-gram chocolate bars was 14.4, but three brands had insect contamination more than twice the average. See the U.S. Food and Drug Administration–Center for Food Safety and Applied Nutrition for Defect Action Levels for food products. Assume that the number of fragments (contaminants) follows a Poisson distribution.

(a) If you consume a 225-gram bar from a brand at the mean contamination level, what is the probability of no insect contaminants?

(b) Suppose that you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level. What is the probability of no insect contaminants?

(c) If you consume seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level, what is the probability that you consume one or more insect fragments in more than one bar?

(d) Is the probability of contamination more than twice the mean of 14.4 unusual, or can it be considered typical variation? Explain.