Forty samples of 100 are taken, with the total number of defective units being 150.
-Calculate $\sigma$ _P, the mean percent defective for all samples collected.

Question

Forty samples of 100 are taken, with the total number of defective units being 150.
-Calculate

\sigma

_P, the mean percent defective for all samples collected.

Quizplus · Accepted Answer

The mean percent defective is calculated as the total number of defectives divided by the total number of units inspected. Here, 150 defectives out of 4000 units (40 samples of 100 each) gives a proportion defective of 0.0375. The standard deviation $\sigma_P$ is calculated using the formula $\sqrt{p(1-p)/n}$, where $p = 0.0375$ and $n = 100$. This results in $\sigma_P = \sqrt{0.0375 \times 0.9625 / 100} = 0.0190$.

Forty Samples of 100 Are Taken, with the Total Number σ\sigmaσ

Forty Samples of 100 Are Taken, with the Total Number $\sigma$