Question

A certain kind of sheet metal has, on average, 5 defects per 20 square feet. Assuming a Poisson distribution, find the probability that a 39 square foot metal sheet has at least 9 defects. Round your answer to four decimals.

Answer 1

Solution:

We are given

Mean = 5 defects per 20 square feet

That is, mean = (5/20) = 0.25 defects per square feet

For 39 square foot metal sheet, mean = 0.25*39 = 9.75

λ = 9.75

We have to find P(X≥9)

P(X≥9) = 1 – P(X≤8)

P(X≤8) = 0.36166

[By using excel command =POISSON(8,9.75,1)]

[You can also find this probability by using Poisson table, Ti-84/83 calculator, or any statistical software.]

P(X≥9) = 1 – P(X≤8)

P(X≥9) = 1 – 0.36166

P(X≥9) = 0.63834

Required probability = 0.6383