1765. To determine the percentage of non-standard items in a batch with a volume of 10000, 500 items were selected, among which 10 were found to be non-standard. Find the sampling error in determining the proportion in cases of with-replacement and without-replacement sampling.
Solution. In the case of repeated sampling $\mu_{\text {d }}=\sqrt{\frac{p(1-p)}{n}} \approx$ $\approx \sqrt{\frac{w(1-w)}{n}}$. According to the condition $w=\frac{10}{500}=0.02$ and $n=500$. Therefore, $\mu_{\text {d }}=\sqrt{\frac{0.02 \cdot 0.98}{500}}=0.00626$.

For sampling without replacement

$$
\begin{gathered}
\mu_{\mu}=\sqrt{\frac{p(1-p)}{n}\left(1-\frac{n}{N}\right)} \approx \sqrt{\frac{w(1-w)}{n}\left(1-\frac{n}{N}\right)}= \\
=0.00626 \sqrt{1-\frac{500}{10000}}=0.00610
\end{gathered}
$$