Question

A certain kind of sheet metal has, on average, 3 defects per 16 square feet.
Assuming a Poisson distribution, find the probability that a 23 square foot metal sheet has at least 4 defects. Round your answer to four decimals.

Answer 1

Since , there are 3 defects per 16 square feet.

Therefore , there are 3/16=0.1875 defect per 1 square feet.

Let , X be the number of defects.

Here , X has Poisson distribution with parameter

Therefore , the probability mass function of X is ,

; ,

= 0 ; otherwise

Here , =0.1875*23=4.3 per 23 square foot.

Now , We want to find the

; From Poisson probability table

Therefore , the probability that a 23 square foot metal sheet has at least 4 defects is 0.6228.