If customers arrive according to a Poisson process with an average arrival rate

Question

If customers arrive according to a Poisson process with an average arrival rate of 10 customers per hour, what is the approximate probability of having more than 10 arrivals in an hour? (Answers are rounded to multiples of 10 - choose closest answer). (Note - this is not a 'Waiting Lines' question that uses the Excel template, but rather is a question about Poisson arrivals and would use the Poisson equation seen in the lab, text and in class. You will most likely require a spreadsheet to be efficient in answering this question).

0.40

0.20

0.50

0.30

a.

0.40

b.

0.20

c.

0.50

d.

0.30

Explanation / Answer

Probability (C=11 I lambda=10)=(10^11)*(e^(-10)) / 11! =0.113

Probability (C=12 I lambda=10)=(10^12)*(e^(-10)) / 12!=0.094

similarly calculate for every next customer till the probability of next customer nears 0 and then sum all the probabilities

You'll get the numbers below

answer is 0.40

Customers Probability 11 0.113736 12 0.09478 13 0.072908 14 0.052077 15 0.034718 16 0.021699 17 0.012764 18 0.007091 total 0.409774

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