if $x_1,x_2,\dots,x_8\sim N(0,52)$, then what is the distribution of $\frac{\bar{x}}{\sqrt{52/8}}$ [closed]

I am trying to find what the distribution for $$x_1$$, $$x_2,\dots, x_8$$ $$\sim$$ $$N(0,52)$$ is. This is a normal distribution question and I'm not adding these probabilities. $$x_1$$, $$x_2,\dots, x_8$$ means there are 8 i.i.d variables.

A $$N(0, \frac{\bar{x}}{\sqrt{52/8}})$$

B $$N(0, \frac{1}{\sqrt{52/8}})$$

C $$N(0,1)$$

D $$(\bar{x},1)$$

E $${\rm Unif}[0,1]$$

I am not sure, but I think the answer is A because that has the mean and standard deviation of the sample.

• Nov 18, 2020 at 19:32
• thanks for the help!
– User
Nov 18, 2020 at 19:53
• You're welcome. Use $\sim$ for $\sim$. Also, please provide context to your question with an edit. Nov 18, 2020 at 20:01
• What is $\bar x$ if it is not the sum of $x_1,\ldots,x_8$ divided by 8?
– Surb
Nov 18, 2020 at 21:14

• @User I don’t think I understand your question then. You have $x1,...,x8$ normally distributed variables and you are looking for the distribution of $(x1,...,x8)$? If that’s the case, that has PDF equal to the product of the PDFs since they are independent, which by the the way is a Gaussian too: math.stackexchange.com/questions/114420/… Nov 18, 2020 at 22:50