A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages?
A)0.0067
B)0.8750
C)0.1755
D)1.0000

Question

Quizplus · Accepted Answer

Since the average rate of emails is 5 per day, we can use the Poisson distribution with a lambda of 5 to find the probability of receiving exactly 5 emails on a given day: P(X=5) = (e^-5)(5^5)/5! = 0.1755 (rounded to four decimal places). Therefore, the correct answer is choice C.

A Statistics Professor Receives an Average of Five E-Mail Messages