In what cases do I use these formulas? 
*

*$$ P (X \leq b) = P\left(Z \leq \frac{b-\mu}{\frac{\sigma}{\sqrt{n}}}\right)$$

*$$P(S_n \leq b) = P\left(Z \leq \frac {b-n\mu}{\sigma\sqrt{n}}\right) $$
Here are two questions which use each formula:
a) An electrical firm manufactures light bulbs that have a length of life that
is approximately normally distributed, with mean equal to 800 hours and a
standard deviation of 40 hours. Find the probability that a random sample
of 16 bulbs will have an average life of less than 775 hours?
b) An average scanned image occupies 0.6 megabytes of memory with a standard
deviation of 0.4 megabytes. If you plan to install 80 images on your
website, what is the probability that their size is between 47 megabytes and
50 megabytes?

The first question uses formula $1$ and the second question uses formula $2$. I don't understand what you look for to apply the specific formula. Any help? 
 A: In the first formula you do not have $X$ but $\overline{X}_n$ which denotes the average. 
Now, start with something simple: If $X_i$ for $i=1,2,\ldots, n$ is i.i.d with mean $μ$ and variance $σ^2$ then according to the CLT the sum $S_n:=\sum_{i=1}^{n}X_i$ is approximately normally distributed with parameters $μ_n=n\times μ$ and variance $σ_n^2=n \times σ^2$. In symbols $$S_n \sim N(nμ, nσ^2)$$ (that is easy to rememeber, or not?). Now (I assume you are familiar with that) you can create a standard normal variable as follows $$Z=\frac{S_n-nμ}{σ\sqrt{n}} \sim N(0,1)\tag{1}$$ This gives you formula 2. Of course $$\overline{X}_n=\frac{S_n}{n}$$ and therefore, if you divide numerator and denominator with $n$ in the above formula you obtain that $$Z=\frac{\frac{S_n}{n}-\frac{\not nμ}{\not n}}{\frac{σ\sqrt{n}}{n}}=\frac{\overline{X}_n-μ}{σ/\sqrt{n}}\sim N(0,1)\tag{2}$$ This gives you formula 1. 
In sum


*

*Remember formula 2. You will use it when you are asked about a probability concerning total (sum of variables).

*Derive formula 1 from formula 2 (there is no need to remember it by heart). You will use when you are asked about a probability concerning average.

