Context
I'm working on a project of computer science to investigate the probablity that a company earns profits in a certain interval. So far, I've got the skewness of my data is $SK=0.72$, $\bar{x}=17.83$ and $SD=1.74$. I want to calculate it But I don't know how to construct the probablity density function of this set of data. I know it must be a skewed curve but I don't know exactly what it's gonna be.
The picture above shows how much money a company earned during six consecutive quarters. I used these to get SD,SK and mean.
Question:
How to get the expected probability ($E[X_i]$) from my data in order to use CLT?
What I thought about this problem:
Denote that PDF $p(x)$, then $p(x)$ satisfies $\int p(x)dx=1$. This is similar to the normal distribution function $N(n,\sigma^2)=\frac{1}{\sigma\sqrt{2\pi}}e^\frac{-(x-\mu)^2}{2\sigma^2}$. And because I have the skewness of my PDF, so I'm thinking about apply it to the normal distribution function to skew its maximum value, but I don't know where to put this number. Also, it seems impossible to make this distribution normal by taking the logarithm of each number.
Edit according to the notes from @emonHR
I was told to try CLT(central limit theorem) it requires the mean and variance which I have now, but also needs the expected value of that probability. I don't know how to get it.
This is my first time dealing with this kind of statistical problems, if any important information is missing or my word is confusing, please tell me.
Any help willl be apreciated. Thanks in advance!