SOLUTION: I am still new at these concepts and am having a hard time figuring out how to solve them. The question states: Farmers Smithers' tractor breaks down on him regularly. In fact, ove

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Question 909196: I am still new at these concepts and am having a hard time figuring out how to solve them. The question states: Farmers Smithers' tractor breaks down on him regularly. In fact, over the last 11 years he's had 18 breakdowns. He believes that the breakdowns occur randomly, but Mrs. Smithers claims otherwise. Complete the following table using basic probability theory and the Poisson distribution. Compare the observed frequency of number of breakdowns per year to the expected number, and decide if you think Farmer Smithers or Mrs. Smithers is right.
#of breakdowns per year How many times this happened Observed frequency of occurrence Expected ""
0 1
1 5
2 3
3 1
4 1
5 0
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
The first thing we will do is assume that our observed frequency of 18 breakdowns over 11 years means we have 18/11 breakdowns every year.
Completing the table
Let X~Poisson(lambda+=+18%2F11)
# times of ef
0 1 1/11 = .0909 P[X=0] = .1947
1 5 5/11 = .4545 P[X=1] = .3186
2 3 3/11 = .2727 P[X=2] = .2607
3 1 1/11 = .0909 P[X=3] = .1422
4 1 1/11 = .0909 P[X=4] = .0582
5 0 0/11 = 0 P[X=5] = .0190