Quality Control A builder ordered two hundred 8-foot grade
Chapter 6, Problem 20E(choose chapter or problem)
Problem 20E
Quality Control 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?
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