# Independent random variables

WY
Hi
I'm wondering if someone can help me out on this question as to how to go about doing it:
X_1, X_2... X_7 are independent random variables represnting a random sample of size 7 from the normal N(10, 7) distribution. Find to 3 dp probablitity that the sample total exceeds 88.

I tried to standardise this but my numbers don't seem to get me the answer of 0.005. Can someone help me out? Thanks in advance :)

How did try to do it? Remember, the d.f. of the sum of random variables with normal distributions is another normal distribution with a mean that is the sum of the means of the individual variables and a variance that is the sum of the variances of the individual variables. Also remember when changing varibles that what appears in the the normal distribution is $$\frac{(x-\mu)}{\sigma}$$ and not $$\frac{(x-\mu)}{\sigma^2}$$, so use the standard deviation and not the variance when changing variables.