EXAMPLE 5.32

Number of potholes. The Automobile Association (AA) in Britain had member volunteers make a 60-minute, two-mile walk around their neighborhoods and survey the condition of their roads and sidewalks. One outcome was the number of potholes, defined as being at least 2 inches deep and at least 6 inches in diameter, in their roads.16 It was reported that Scotland averages 8.9 potholes per mile of road and London averages 4.9 potholes per mile of road. Suppose that the number of potholes per mile in each of these two regions follow the Poisson distribution. Then

  • • The number of potholes per 20 miles of road in Scotland is a Poisson random variable with mean

  • • The number of potholes per half mile of road in London is a Poisson random variable with mean

  • • The number of potholes per 500 miles of road in Scotland is a Poisson random variable with mean

  • • If we examined 2 miles of road in Scotland and 5 miles of road in London, the total number of potholes would be a Poisson random variable with mean