# Trouble with samples in a normal distribution

I'm okay with solving regular normal distribution questions (where $X$ is a normal random variable with mean $\mu$ and standard deviation $\sigma$). However, we're currently dealing with samples within a larger population and I'm struggling to understand how the process of solving a question goes.

Here's an example:

The weight of a car is normally distributed with a mean of $2500$ and a standard deviation of $50$. Next, a random sample of $5$ cars is taken. What is the standard error of the sample mean?

I know that the standard error of the sample is:

$$\frac{\sigma^2}{n}$$

but a question can't be this easy to answer can it? It's leading me to believe I'm missing a concept. If someone would be able to walk through the procedure of solving a question of this nature it would be greatly appreciated.

• The question is in fact that simple. $\frac{\sigma^2}{n}$ is the standard error of the sample mean. "standard error of the sample" (what you said it is) doesn't make any sense. – Jonathan Christensen Nov 11 '12 at 2:19

The sample mean $M$ of a sample of size $n$ from a normally distributed RV with mean $\mu$ and variance $\sigma^2$ is a RV $\sim N(\mu,\sigma^2/n)$. The standard error of the mean $s_M$ is the standard deviation of the sample mean and so $s_M=\sigma/\sqrt{n}$.