A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

Step-by-step explanation:

We have the mean during an interval, so the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive.

This means that

Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

This is P(X = 3). So

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.