A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?
A) binomial distribution
B) Poisson distribution
C) hypergeometric distribution
D) None of the above.

Question

Quizplus · Accepted Answer

A Poisson distribution should be used because it models the number of events (in this case, emails) occurring in a fixed interval of time (one day). The events must be rare and independent, which is reasonable to assume for the number of emails a professor receives from students. The binomial distribution assumes a fixed number of trials, each with a binary outcome, which is not appropriate for this scenario. The hypergeometric distribution is used when the sample is drawn without replacement from a finite population, which does not apply here either.

A Professor Receives, on Average, 24