a.) Draw the graph of the straight line with equation $y = 2x + 1$. Now assume that a company has several shops. Let $Y_i$ be the profit the shop number $i$ makes in the coming year. Let $x_i$ be the size of the shop number $i$. We assume that for all these shops the following relationship holds. $Y_i = 2x_i + 1 + \epsilon_i$ where $\epsilon_i$ is a random term for which $E[\epsilon_i] = 0$ and such that $\epsilon_1,\epsilon_2,...$ are $i.i.d$. So, if $\alpha = 2$ and $\beta = 1$, we can write $Y_i = \alpha + \beta x_i +\epsilon_i$.
Now, the company plans to open a new shop with size 3. What is the expected profit for that shop? Also, write it in terms of $\alpha$ and $\beta$. What does the straight line $y = \alpha + \beta x$ represent?
b.) Assume that the errors are normal and that it is known that the standard deviation of $\epsilon = 2$ for all shops. Give a $95 \%$-confidence interval for the profit of that shop with size 3.
For part a, I drew the graph which is the easy part , but I do not know what it represents or how to do the problem.
For part b, I know that the profit of the shop is going to be a normal with known expectation and standard deviation, so the confidence interval is simple expected value plus/minus standard deviation times $c$, where $c$ is the constant so that $P(-c \le N(0,1) \le c) =0.95$
but then I get lost on what I have to do next.