Question 1044465: A company which supplies ready mix concrete receives, on average, 6 orders per day.
A) What is the probability that, on a given day:
(i) No orders are received?
(ii) No more than 2 orders are received?
(iii) At least 3 orders are received?
B) What is the probability that, on a given half-day, no orders are received?
C) What is the mean and standard deviation of orders received per day?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Fits with poisson distribution where it is discrete, proportional to time, random, and could theoretically be infinite although unlikely.
The poisson parameter is 6.
p(0)=e^(-6)6^0/0!
That is e^(-6)=0.0025
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no more than 2 is 0,1,2
p(1)=e^(-6)*6/1!=0.0149
p(2)=e^(-6)*6^2/2!=18*e^(-6)=0.0446
The sum of those 3 is 0.0620
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At least 3 is 1-the above probability, since that is the complement. It will be 0.9380.
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At a given half day lambda=3
p(0)=e^(-3)=0.0498
Mean and variance are the same, and they are both the parameter lambda, here 6 orders for the mean and sqrt (6) or about 2.45 orders for sd.
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