Question

Which situation is best modeled by a Poisson distribution?

a. Suppose a crate contains 96 eggs, 12 of which are broken. A baker examines 20 different eggs from the carton. What is the probability that he will find three or more broken eggs?
b. On average, one person calls in sick each week at a business called Acme Motors. What is the probability that no one will call in sick next week?
c. Suppose that the city bus arrives at six-minute intervals. What is the probability that a passenger will have to wait more than 10 minutes for a bus?
d. Suppose that the probability is 35% that an individual can be coerced into giving someone else a severe electric shock.
e. A researcher conducts the experiment until she finds one such person. What is the probability she will require more than four subjects?
f. What is the probability that 10 of the next 15 rolls of a pair of dice will result in a either a 7 or 12?

Answer 1

Option b, regarding the likelihood of no one calling in sick at a business within a week where on average one person calls in sick weekly, is best modeled by a Poisson distribution.

Step-by-step explanation:

The scenario that is best modeled by a Poisson distribution is option b. This situation describes the probability of a certain number of events (in this case, people calling in sick) occurring within a fixed interval of time (one week) based on a known average rate (one person per week) and assuming each event is independent.

In contrast, a is better modeled by a hypergeometric or binomial distribution since the number of broken eggs in a fixed number of trials (eggs examined) is being determined. c considers waiting time and is better modeled by an exponential distribution. d is regarding a probability of an individual act which is not based on a rate over time. e is related to finding the first success, and f is about the probability of outcomes for rolls of dice, which implies a binomial distribution with multiple trials.