Question

Suppose x has a normal distribution with mean μ = 47 and standard deviation σ = 3. Describe the distribution of x values for sample size n = 4. (Round σx to two decimal places.)

Answer 1

Answer:

$\mathbf{\bar{X}\sim N\left ( 47,1.50 \right )}$

Step-by-step explanation:

The sample mean $\bar{x}$ follows with mean $\mu$ and standard deviation $\dfrac{\sigma}{\sqrt{n}}$

Thus, the mean is:

$\mu_{\bar{X}} = \mu = 47$

And standard deviation is:

$\begin{aligned}\sigma_{\bar{X}} &=\dfrac{\sigma}{\sqrt{n}}\\ &=\dfrac{3}{\sqrt{4}}\\&=1.5\end{aligned}$