Normal Distribution: Definition, Formulas, and Example Problems

Normal Distribution: Definition, Formulas, and Example Problems The normal distribution is one of the discussions in statistics related to the probability distribution (probability distribution). Of course you already know about the distribution of a discrete variable and a continuous variable. This normal distribution is one of the distributions of a continuous variable. In the following, we will describe the normal distribution first.

Definition of Normal Distribution

What is a normal distribution? Normal distribution is one type of distribution with continuous random variables. In a normal distribution there is a curve/graph that is depicted as a bell shape. The normal distribution is also known as the Gaussian distribution. One of the equations contained in the normal distribution is related to the density function. The following is a density function in a normal distribution.
Normal Distribution Formula: $$f(x)=\frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$$ Information:
$x$: Data element.
$\pi$: Constant pi is 3.1415...
$e$: Number of natural is 2.71828...
$\mu$: Average data
$\sigma$: Standard Deviation of Data
How to calculate z value? The z value can be calculated by the following formula: $$z=\frac{x-\mu}{\sigma}$$
In the previous section, it was explained that data with a normal distribution had a bell-shaped curve. The shape of the curve of normally distributed data is as follows.

Based on the normal distribution curve above, the normal distribution has an average (mean) equal to 0 and a standard deviation equal to 1. The following will explain some examples of the application of the normal distribution.

Application of Normal Distribution

The normal distribution is very important to study, especially in analyzing statistical data. With data taken at random and normally distributed, it will be easier to analyze and predict and draw conclusions for a wider scope. The normal distribution is widely applied in various statistical calculations and modeling which is useful in various fields. In determining the probability distribution, it is easier for us to use Microsoft Excel because the calculation will be automatic. Using the formula =NORMDIST(x;mean;standard_dev;cumulative), you can see more details at Original Source.
The following are examples of questions related to group distribution to improve your understanding.
Example of Group Distribution Problem
In an exam there are 300 students who take the exam. The average of the test results is 70 and the standard deviation of the test results is 10. If the student's test score data is normally distributed, then what percentage of students get an A if the requirement to get an A is a score of more than 85.
Solution:
Based on the example questions above, the following information is obtained.
$\mu$ = 70
$\sigma$ = 10
$x$ = 85
will specify $Z(X>85)$. You use the formula: =1-NORMDIST(85;70;10;TRUE)
So, $Z(X>85)=0.0668$ = 6.68%.
Thus this post, see you and happy learning.

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