Question

A supermarket has three entrance doors. It is assumed that the number of people who come...

A supermarket has three entrance doors. It is assumed that the number of people who come daily for each of the doors are independent and follow a Poisson distribution of means 300, 150 and 50, respectively.

a) What is the distribution of the total number of people who enter at the supermarket daily?
b) What is the probability that in 200 days the influx exceeds the 40260?
Math   Statistics-And-Probability   
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Answer #1

a) Distribution of the total number of people who enter at the supermarket daily is again poison with mean is equal to

    300+1500+50=500 people. It is simply addition of three indepedent poison.

b) for t=200 days the required probability is given by -

P ( Y > 40260), where Y is number of people enter in 200 days. that is with rate= 500*200=100000

After calculation of all quantities using r-software, the result is

P (Y >40260) = 1- 0 = 1

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