A statistics professor finds that when he schedules an office hour at the 10:30a, time slot, an average of three students arrive. Find the probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive

The probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.

Step-by-step explanation:

Let X = number of students arriving at the 10:30 AM time slot.

The average number of students arriving at the 10:30 AM time slot is, λ = 3.

A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables. For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.

The random variable X is also a Poisson random variable because it represents the fixed number of students arriving at the 10:30 AM time slot.

The random variable X follows a Poisson distribution with parameter λ = 3.

The probability mass function of X is given by:

Compute the probability of X = 2 as follows:

Thus, the probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.

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step-by-step explanation:

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both equations and proportions are better.