A population has standard deviation 12. The standard error of the mean for random samples of size 36 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
The standard error of the mean is the standard deviation of the sampling distribution of the sample mean:
\( \displaystyle \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \)
With \(\sigma = 12\) and n = 36:
\( \displaystyle \sigma_{\bar{x}} = \frac{12}{\sqrt{36}} = \frac{12}{6} = 2 \)
Why the other options are incorrect
Option (1) \( \displaystyle\frac{1}{3} \) — Incorrect. This is 12 ÷ 36, dividing by n instead of \(\sqrt{n}\).
Option (2) 6 — Incorrect. This is only \(\sqrt{36}\), the divisor.
Option (3) 72 — Incorrect. This is \(12 \times 6\), multiplying by \(\sqrt{n}\) instead of dividing.