# How can you estimate the parameters of a normal distribution?

Use the sample mean $\overline{x}$ and the sample standard deviation $s$ to estimate the mean $\mu$ and standard deviation $\sigma$ of the normal distribution you wish to use.
The normal distribution has probability density function (pdf) $f \left(x\right) = \frac{1}{\sigma \sqrt{2 \pi}} {e}^{- {\left(x - \mu\right)}^{2} / \left(2 {\sigma}^{2}\right)}$. The parameter $\mu$ is its mean and the parameter $\sigma$ is its standard deviation.
If you have data from a random sample and compute the sample mean $\overline{x} = \frac{{x}_{1} + {x}_{2} + {x}_{3} + \cdots + {x}_{n}}{n}$ and the sample standard deviation $s = \sqrt{\frac{{\left({x}_{1} - \overline{x}\right)}^{2} + {\left({x}_{2} - \overline{x}\right)}^{2} + \cdots + {\left({x}_{n} - \overline{x}\right)}^{2}}{n - 1}}$, these will be good estimates for $\mu$ and $\sigma$ when your sample size $n$ is sufficient large.