Certified Quality Engineer (CQE) Practice Exam 2026 - Free Quality Engineer Practice Questions and Study Guide

To determine the probability that nonconforming pieces will not be found in a sample of 50 when the process produces a rate of 0.2% nonconforming pieces, we first express the nonconforming rate as a decimal: 0.2% is equivalent to 0.002. This means that the probability of a piece being conforming is 1 - 0.002, which equals 0.998.

Since we want to find out the probability that all 50 pieces in the sample are conforming, we can use the following formula for independent events:

Probability(all conforming) = (Probability of a conforming piece) ^ (number of pieces in the sample)

Thus, we calculate:

Probability(all conforming) = 0.998^50

When you calculate this:

0.998^50 ≈ 0.91

This shows a strong probability that no nonconforming pieces will be present in the sample of 50. Therefore, option D, which brings this probability into the context of 0.91, accurately represents the situation where, despite a small percentage of nonconforming pieces, the likelihood of selecting a sample of 50 and finding none is quite high.