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# Statistics 2 (stinky) watch

1. In a county, there are on average 1.8 potholes per 100m of roadway. Calulate the probablity that there are fewre than 3 potholes in each of the 5 randomly chosen 200m streches of the countries roadways. (ans 0.00254)

Any help? I keep getting 0.2047.......but when im doing the question it just *feels* wrong
2. (Original post by orange soap)
In a county, there are on average 1.8 potholes per 100m of roadway. Calulate the probablity that there are fewre than 3 potholes in each of the 5 randomly chosen 200m streches of the countries roadways. (ans 0.00254)

Any help? I keep getting 0.2047.......but when im doing the question it just *feels* wrong
Use Poisson:

X~Po(1.8)

5 stretches of 200m means 10 stretches of 100m, so r=10.

For a 200m strip, the mean would be 1.8*2 = 3.6, use the Poisson formula thingy with r=5.
4. (Original post by orange soap)
In a county, there are on average 1.8 potholes per 100m of roadway. Calulate the probablity that there are fewre than 3 potholes in each of the 5 randomly chosen 200m streches of the countries roadways. (ans 0.00254)

Any help? I keep getting 0.2047.......but when im doing the question it just *feels* wrong
Define X as the number of potholes in a 200m stretch. Then, the average is 1.8*2=3.6, so we have X~Po(3.6). Then find P(X < 3) and raise that to the power 5, because we need all 5 of the selected stretches to have fewer than 3 potholes. I hope that gives the right answer!

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