A builder ordered two hundred 8-foot grade A 2-by-4s for a construction job. To qualify as a grade A board, each 2-by-4 will have no knots and will average no more than 0.05 imperfection per linear foot. The following table lists the number of imperfections per 2-by-4 in the 200 ordered:

x (number of imperfections) Frequency

0...............................................................124

1.................................................................51

2.................................................................20

3...................................................................5

(a) Construct a probability distribution for the random variable X, the number of imperfections per 8 feet of board, assuming that it follows a Poisson process with λ = 0.05 and t = 8.

(b) Compute the expected number of 2-by-4s that will have 0 imperfections, 1 imperfection, and so on.

(c) Compare these results with the number of actual imperfections. Does it appear the 2-by-4s are of grade A quality? Why?