A statistics professor finds that when he 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 6.

If we use the probability mass function we got:

Step-by-step explanation:

Previous concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

Solution to the problem

Let X the random variable that represent the number of students arrive at the office hour. We know that

The probability mass function for the random variable is given by:

And f(x)=0 for other case.

For this distribution the expected value is the same parameter

And we want this probability:

If we use the probability mass function we got:

x=6 and x=3

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