Public Health and Nutrition
The mean number of commercially prepared meals per week for a typical American is 4.39 This might seem a little high. But consider young professionals who eat lunch out several times each week, and families that order out for pizza or stop at a fast-food restaurant routinely.
a. What is the probability that a randomly selected American does not eat out during a week? Eats out once during the week? Twice during the week?
b. Suppose two Americans are selected at random. What is the probability that the total number of meals for the two Americans during a week is 0? 1? 2?
c. Suppose the mean number of times an American eats out during a two-week period is 8. What is the probability that a randomly selected American does not eat out during a two-week period? Once during the two-week period? Twice during the two-week period?
d. How do your answers in parts (b) and (c) compare? What property does this suggest about a Poisson random variable?