EXAMPLE 5.18 Paint Finish Flaws

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Auto bodies are painted during manufacture by robots programmed to move in such a way that the paint is uniform in thickness and quality. You are testing a newly programmed robot by counting paint sags caused by small areas receiving too much paint. Sags are more common on vertical surfaces. Suppose that counts of sags on the roof follow the Poisson model with mean 0.7 sag per square yard and that counts on the side panels of the auto body follow the Poisson model with mean 1.4 sags per square yard. Counts in nonoverlapping areas are independent. Then

  • The number of sags in two square yards of roof is a Poisson random variable with mean .
  • The total roof area of the auto body is 4.8 square yards. The number of paint sags on a roof is a Poisson random variable with mean .
  • A square foot is 1/9 square yard. The number of paint sags in a square foot of roof is a Poisson random variable with mean .
  • If we examine one square yard of roof and one square yard of side panel, the number of sags is a Poisson random variable with mean .