Defects in marble countertops usually require the whole top to be reconstructed.In one kitchen shop, the percent defective in the past has been one percent.If a sample size of 30 is taken, what should the 95.5 percent upper control limit be?
A)0.030
B)0.000
C)0.046
D)0.064

Question

Quizplus · Accepted Answer

To find the upper control limit (UCL), we use the formula:
UCL = p̂ + zα/2 * sqrt(p̂(1-p̂)/n)
where p̂ is the sample proportion, zα/2 is the z-score corresponding to the desired confidence level (95.5%), and n is the sample size.

In this case, p̂ = 0.01 (1%), zα/2 = 2.004 (from a standard normal distribution table), and n = 30. Plugging these values into the formula, we get:
UCL = 0.01 + 2.004 * sqrt(0.01*0.99/30)
UCL ≈ 0.046

Therefore, the best choice is C, with an explanation as shown above.

Defects in Marble Countertops Usually Require the Whole Top to Be