Question 1170266: In a food processing and packing plant, there are on average two packing machine breakdowns per week.
a) (2 marks) Determine the mean and the standard deviation of the distribution.
b) (2 marks) What is the probability that there are no machine breakdowns during a given week?
c) (4 marks) What is the probability that there are at most two machine breakdowns during a given week?
d) (3 marks) What is the probability that there are exactly three machine breakdowns during the next two weeks?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! would assume a Poisson both because likely to be a large number of such machines and also because there is no way to calculate the probability without being given the sd, unless there is a binomial, Poisson distribution, or a proportion where the two are dependent.
The mean and variance are both 2, so the sd is sqrt(V)=sqrt(2) or 1.414
P(0)=e^(-2)2^0/0!=0.1353
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at most 2 is 0,1,2
probability of 1 is e^(-2)*2^1/!=0.2707
for 2 it is e^-2)*2^2/2!=0.2707
the probability is 0.6767
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for 3 in 2 weeks it is equivalent of parameter 4 for that time period, since the distribution is proportional to time. e^(-4)^4^3/3!=0.1954
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