Question 1194910: A bank manager wants to provide fast customer service at the bank counter. Currently the bank can serve up to 10 customers for a period of 15 minutes without significant delay. The average speed of arrival is 7 customers for a period of 15 minutes. Let x be the number of customers who arrive in a 15-minute period. Assuming x has Poisson distributions,
a) Find the probability that 10 customers will arrive in a certain 15-minute period.
b) Find the probability that there will be significant waiting at the counter during a certain 15-minute period.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The probability that 10 will arrive, given a Poisson distribution with parameter 10 is
e^(-10)*10^10/10!=0.1251
The probability of 10 or fewer is 0.5830 ((poissoncdf function looking at interval [0, 10]
So the probability of having more than this with significant waiting is the complement, or 0.4170.
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