AP Statistics · Unit 5 · Sampling Distributions

A semiconductor foundry processes large batches of silicon wafers through a high-temperature anneal furnace. Based on years of production records, the population proportion of wafers that develop a visible surface defect during the anneal is $p = 0.08$. A quality control inspector plans to randomly select $n = 150$ wafers from an anneal run and record $\hat{p}$, the sample proportion of wafers with a visible defect, to monitor whether the furnace is operating normally.

(a) Describe the sampling distribution of $\hat{p}$ for random samples of 150 wafers from this anneal run. Justify the shape you give.
(b) Assuming the furnace is operating normally, would it be surprising for an inspector to observe $\hat{p} = 0.11$ or more in a random sample of 150 wafers? Justify your answer, using the fact that $P(Z \geq 1.35) \approx 0.0885$.
(c) Suppose the inspector instead samples only 20 wafers from each anneal run. Explain how this changes the standard deviation of $\hat{p}$, and whether a Normal approximation like the one in part (b) could still be used.