SOLUTION: A math professor finds that when he schedules an office hour for student help, an average of 1.5 students arrive. Find the probability that in a randomly selected office hour, the

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Question 1192724: A math professor finds that when he schedules an office hour for student help, an average of 1.5 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 6.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

This uses the Poisson Distribution.
More info can be found here:
https://online.stat.psu.edu/stat414/book/export/html/678

lambda = greek letter lambda
lambda = 1.5 = average number of arrivals per hour

P(x) = probability of having exactly x arrivals (x = 0, x = 1, x = 2, ...)
P(x) = %28e%5E%28-lambda%29%2Alambda%5Ex%29%2F%28x%21%29
The exclamation mark indicates factorial. Example: 5! = 5*4*3*2*1 = 120.
The 'e' refers to the special constant e = 2.718...

Plug in lambda = 1.5 and x = 6
P(x) = %28e%5E%28-lambda%29%2Alambda%5Ex%29%2F%28x%21%29

P(6) = %28e%5E%28-1.5%29%2A%281.5%29%5E6%29%2F%286%21%29

P(6) = 0.00352998886172 which is approximate.

Answer: Approximately 0.0035
This is about a 0.35% chance.