What is the rule of $1.96$ for estimating confidence intervals? I have a sequence of A/B currency exchanges for some days. With that data I can calculate the daily returns, and that's what I did. I need to calculate the confidence interval for the expected daily returns of the A/B currency exchange by using the $1.96$ rule.
What is this $1.96$ rule? Why exactly that number? Why is it related to compute confidence intervals? So, how can we use it in general to compute confidence intervals?
There's an article on Wikipedia, but honestly I am not understanding it, and why it is related to the calculation of the confidence interval of the expectation.
Note that for now I am not asking specifically about how to solve my problem, but how what I am asking about is related to my problem (after answering those questions).
 A: The value of $1.96$ stems from the fact that we generally use 5% significance level in computing the confidence interval or any hypothesis testing.
When we are looking for a two sided confidence interval of mean, we want to find the a value less than the sample mean, let it be $LL$ and another value above the sample mean, let's call it $UL$. Now these values are chosen in a manner that when sampled large number of times, the true mean will lie between these values 95% of the time.
Mathematically, $P(LL \leq \mu \leq UL) = 0.95$
Now suppose sample mean, $\bar{X} = 0$ and $\sigma = 1$ (That is sampling from N(0,1)). In this case if we want to estimate the true mean $\mu$, what should our $UL$ and $LL$ be?
By using the normal tables, we can see that $P(z \leq 1.96) = 0.975$ and $P(z \leq -1.96) = 0.025$.
Thus, $P(-1.96 \leq \mu \leq 1.96) = 0.95$
Similarly, for non standard cases,
${P(-1.96 \leq \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} \leq 1.96) = 0.95}.$
Or, ${P(\bar{X}-1.96 \frac{\sigma}{\sqrt{n}} \leq \mu \leq \bar{X}+1.96 \frac{\sigma}{\sqrt{n}}) = 0.95}.$ 
Thus, we write the confidence interval as $\bar{X} \pm 1.96 \frac{\sigma}{\sqrt{n}}.$
This value would be different if we need confidence interval at some other significance levels. For instance, for 99% confidence interval we shall use $2.576$
