Question

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

Answer 1

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

$P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...$

Compute the probability that on a randomly selected day she will have five messages as follows:

$P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}$

               $=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755$

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.