Why is normal distribution important?

Hint: We first describe the importance of the normal distribution and the components of its PDF. The use of mean and the standard deviation for the formula makes it unique for real life implications.

Complete step-by-step solution:
A normal distribution is a distribution that is solely dependent on two parameters of the data set: mean and the standard deviation of the sample.
Mean is the centre of the curve. This is the highest point of the curve as most of the points are at the mean. There is an equal number of points on each side of the curve. The centre of the curve has the greatest number of points. This allows us to easily estimate how volatile a variable is and given a confidence level, what it's likely value is going to be.
The probability density function of the normal distribution is $f\left( x \right)=\dfrac{1}{\sigma \sqrt{2\pi }}{{e}^{-\dfrac{1}{2}{{\left( \dfrac{x-\mu }{\sigma } \right)}^{2}}}}$ where $\mu $ is the mean and $\sigma $ is the standard deviation of the sample.

Note: The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution. It is also known as the Gaussian distribution and the bell curve.