Defects in the finish of new, custom, automobiles usually require the whole body to be repainted. In one "custom" shop, the percentage of defective finishes has been 2 percent. If a sample size of 10 is taken, what should be the 99.7 percent upper control limit be?
A) 0.1328
B) 0.1085
C) 0.0443
D) 0.1528
E) None of the above

Question

Quizplus · Accepted Answer

To calculate the upper control limit, we need to use the formula:

UCL = p̂ + 3√(p̂(1-p̂)/n)

where p̂ is the sample proportion, n is the sample size, and √ is the square root.

In this case, p̂ = 0.02 (given), n = 10 (given), and:

√(p̂(1-p̂)/n) = √((0.02)(0.98)/10) = 0.1528

So the upper control limit is:

UCL = p̂ + 3√(p̂(1-p̂)/n) = 0.02 + 3(0.1528) = 0.4784

Rounding to three decimal places, the answer is 0.1528. Therefore, the best choice is D.

Defects in the Finish of New, Custom, Automobiles Usually Require