A machine that produces a major part for an airplane engine is monitored closely. In the past, 6% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is
A) 70.
B) 69.
C) 135.
D) 136.

Question

Quizplus · Accepted Answer

The sample size needed for a proportion can be calculated using the formula $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the desired confidence level (1.96 for 95% confidence), $p$ is the proportion (0.06 in this case), and $E$ is the margin of error (.04). Plugging in the values gives $n = \frac{(1.96)^2 \cdot 0.06 \cdot 0.94}{(0.04)^2} \approx 135.29$. Since sample size must be a whole number, we round up to 136.

A Machine That Produces a Major Part for an Airplane