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 the 99.7 percent upper control limit be?
A)0.1328
B)0.1085
C)0.0443
D)0.1528

Question

Quizplus · Accepted Answer

The 99.7% upper control limit for defects in a process can be calculated using the formula for the upper control limit (UCL) in a binomial distribution, which is UCL = p + Z√(p(1-p)/n), where p is the proportion of defects (0.02 in this case), n is the sample size (10), and Z is the Z-value corresponding to the desired confidence level (99.7% confidence level corresponds to a Z-value of approximately 3, considering the empirical rule or looking up a Z-table for a more precise value). Plugging in the values: UCL = 0.02 + 3√(0.02*0.98/10) ≈ 0.02 + 3*0.0443 ≈ 0.1528.

Defects in the Finish of New, Custom Automobiles Usually Require