Expected value of a sample

Question

I am unsure of how to solve this question. I know from examples questions that expected value of a sample is usually very close to the population mean. However, it says to compute the expected value and I don't know how to do that or how to find the sample's standard deviation. I have tried going through various statistics textbooks, but I cannot find an example to solve this question:

Answer 1

HINT: You know that $X\sim N(2.835,0.15^2)$, assuming that $X_1,...X_{100}$ is a random sample of $X$ then $$E[\overline{X}]=\frac{1}{n}\sum_{i=1}^{100}E[X_i]$$

$$Var(\overline{X})=\frac{1}{n^2}\sum_{i=1}^{100}Var(X_i)$$

I do not know what you've learned but if $X\sim N(\mu,\sigma^2)$ then $\overline{X}\sim N(\mu,\frac{\sigma^2}{n})$

If you are learning about inference, I recommend to take a look at some of these 2 books

Statistical Inference

Introduction to the Theory of Statistics

EDIT: $E[\overline{X}]=\frac{1}{100}\sum_{i=1}^{100}E[X_i]=\frac{1}{100}(E[X_1]+E[X_2]+\cdots+E[X_{100}])=\frac{1}{100}100*E[X_1]=2.835$ where the last equality comes from the fact of the independence of the variables