Discussion
The standard error of sample mean based on 100 observations from normal distribution with mean 50 and standard deviation 5 is ............ .
Answer: A
The standard error is 1/2.
The standard error of the mean is the population standard deviation divided by the square root of the sample size:
\[ \begin{aligned} SE(\bar{x}) &= \frac{\sigma}{\sqrt{n}} = \frac{5}{\sqrt{100}} \\ &= \frac{5}{10} = \frac{1}{2} \end{aligned} \]
The mean of 50 plays no part. 1/20 is what you get by dividing 5 by n instead of by its square root, and 1/100 and \(1/\sqrt{2}\) do not follow from the formula at all.
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