Normal Distribution
Child: Imagine you and your friends are lining up according to your heights. If most of you are of average height, you’d be in the middle, with the shorter and taller ones at the ends. If we drew a line above your heads, it would look like a bell or a hill. That’s what we call a “normal distribution”.
Teenager: Think about grades in your class. Some students get high grades, some get low grades, but most get grades somewhere in the middle, right? If you draw a graph with grades on the bottom and the number of students on the side, the graph will look like a hill or a bell shape. This is what we call a normal distribution.
Undergrad majoring in the same subject: In statistics, a normal distribution is a type of continuous probability distribution for a realvalued random variable. The graph of the normal distribution is characterized by its bell shape, with the peak at the mean value, and it is symmetric around the mean. A lot of natural phenomena follow a normal distribution, like people’s heights or IQ scores.
Grad student: The normal distribution, or Gaussian distribution, is a fundamental concept in statistics and is often used in the natural and social sciences for realvalued random variables. It’s characterized by two parameters, the mean (mu) and standard deviation (sigma). The mean indicates where the bell is centered, and the standard deviation determines the width of the bell. The properties of normal distribution, such as the 689599.7 rule, are crucial in hypothesis testing and confidence interval estimation.
Colleague (Fellow Researcher/Engineer): As you know, the normal distribution is central to many statistical procedures and theories, thanks to the Central Limit Theorem. The CLT states that the sum of a large number of independent and identically distributed random variables, irrespective of their shape, will approximately follow a normal distribution. This property makes the normal distribution very tractable analytically, which is why it’s widely used in fields like machine learning, finance, and physics.
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric about the mean and defined by two parameters  the mean μ and the standard deviation σ.
Some key properties:
 Bell shaped and symmetric about the mean
 Mean, median and mode are all equal
 About 68% of values fall within 1 standard deviation of the mean
 About 95% within 2 standard deviations
 Probabilities can be calculated using the PDF f(x) = (1/(σ√(2π)) * e^(0.5*(xμ/σ)^2)
It is one of the most important distributions in statistics and is used to model many natural phenomena.
Example in Java:


This samples a random value from a N(10, 4) distribution by using the Gaussian distribution in Java’s Random class.
Examples in C++ and Python follow a similar approach of using inbuilt random number generators for normal distribution. The standard normal can be generated and transformed to any normal distribution.
Description
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing up in the form of a bell curve.
It is characterized by two parameters  mean and standard deviation. About 68% of values lie within 1 standard deviation of the mean.
Normal distribution occurs frequently in natural processes due to the central limit theorem. Many measurements like heights and test scores follow normal distribution.
It is useful for modeling phenomena like measurement errors.
Solution
Here is code to generate normally distributed random numbers:
Java


C++


Python


Normal distribution provides a good model for natural phenomena like heights, errors etc.
Description: Normal Distribution
The Normal Distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean. It’s often represented by a bellshaped curve. It is fully characterized by its mean and standard deviation. In a normal distribution, about 68% of the data falls within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Solution:
You can generate a set of numbers that follow a normal distribution using programming languages. Let’s look at how to generate a series of random numbers that form a normal distribution in Java, C++, and Python.
Java
In Java, you can use the Random
class to generate normally distributed numbers.


C++
In C++, you can use the <random>
library to generate normally distributed numbers.


Python
In Python, you can use the numpy
library to generate normally distributed numbers easily.


Key Takeaways:
 The Normal Distribution is defined by its mean and standard deviation.
 Different programming languages provide ways to generate normallydistributed random numbers.
 Libraries like
numpy
in Python make it very easy to generate these numbers.  In C++ and Java, you will often have to use additional libraries or builtin functions to achieve the same.