Question

10) 12 POINTS Poisson Problem Area Manufacturing Your Company pours housing foundations and driveways. The company generates one blemish for every 2000 square feet covered. You must negotiate with a construction superintendent on the total quality of your company's work. The pouring will be 150 feet by 120 feet. What is the expected value (m) for the defects in this job? What is the probability that you would have exactly 10 defects in this job? What is the probability that you would have 10 or less defects in this job? What is the probability that you would have more than 10 defects in this job? The superintendent wants to reject your company's work if more than 15 defects are found. What is the probability that your company's work will be rejected? Is this an acceptable risk?

Answer 1

1)

expected value λ=1*150*120/2000 =9

2)

P(X=10)=

{e-λ*λx/x!}=

0.1186

3)

P(X<=10)=

∑x=010 {e-λ*λx/x!}=

0.7060

4)

P(X>11) =1-P(X<=10) =1-0.7060 =0.2940

5)

P(X>15)=1-P(X<=15)=

1-∑x=015 e-λ*λx/x!=

0.0220

6)

yes since probability of above happening is low if the defect rate given above is correct