A manufacturing process produces computer chips in batches of 100. The firm believes that the percent of defective computer chips is 2%. If in five batches the percent of chips defective were 3%, 8%, 1%, 2%, and 7%, how many of these fell outside of the upper or lower control limits for the proportion of defective computer chips in a batch?
A) 0
B) 1
C) 2
D) 3

Question

Quizplus · Accepted Answer

The control limits for a proportion are calculated as p ± 3√(p(1-p)/n), where p is the average proportion defective (0.02) and n is the batch size (100). Calculating this gives control limits of approximately 0.02 ± 0.0346, or between -0.0146 and 0.0546. Since negative proportions are not possible, the lower limit is effectively 0. Therefore, any batch with a defect rate above 5.46% is out of control. The batches with 8% and 7% defect rates are outside this limit.

A Manufacturing Process Produces Computer Chips in Batches of 100