3. (10 points) In older cities across North America, infrastructure is deteriora

Question

3. (10 points) In older cities across North America, infrastructure is deteriorating, including water lines that supply homes and businesses. A report to a city council stated that there are on average 10 water line breaks per 100 kilometers per year in the city. Outside the city, the average number of breaks is7 per 100 kilometers per year. a. Find the probability that in a stretch of 200 kilometers in a city there are 15 or more breaks next year. b. Find the probability that there are 5 or fewer breaks in a stretch of 50 kilometers outside the city next year.

Explanation / Answer

Given inside city  

Average=10 per 100 km ie 20 for 200 km

Outside city 7 per 100 km ie 3.5 for 50 km

a)

We need 15 or more in 200 km

P(X<15)=1-e^(-20*1)=1-e^-20

So P(X>15)=1-[1-e^-20]= e^-20

ie nearly 0% probability

b)

P(X<5) in 50 km

=1-e^-3.5=0.9698

ie 96.98% probability

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