# Standard Normal Distribution (SND) – Java Program

The standard normal distribution is a special case of the normal distribution. It occurs when a normal random variable has a **mean of 0** and a **standard deviation of 1**. The normal random variable of a standard normal distribution is called a **standard score** or a **z score**.

A conversion from Normally distributed to Standard Normally distributed value occurs via the formula,

Z = (X - u) / s where:Z= value on the standard normal distributionX= value on the original distributionu= mean of the original distributions= standard deviation of the original distribution

**Code –**

`// Java code to demonstrate the naive method` `// of finding Z-value` ` ` `import` `java.io.*;` `import` `java.util.*;` ` ` `class` `SDN {` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` ` ` `// initialization of variables` ` ` `double` `Z, X, s, u;` ` ` `X = ` `26` `;` ` ` `u = ` `50` `;` ` ` `s = ` `10` `;` ` ` ` ` `// master formula` ` ` `Z = (X - u) / s;` ` ` ` ` `// print the z-value` ` ` `System.out.println(` `"the Z-value obtained is: "` `+ Z);` ` ` `}` `}` |

**Output –**

the Z-value obtained is: -2.4

**Generating a Random Standard Normal Function – Using nextGaussian() in Java :**

The **nextGaussian()** method is used to get the next random, Normally distributed double value with mean 0.0 and standard deviation 1.0.

Declaration :public double nextGaussian()Parameters :NAReturn Value :The method call returns the random, Normally distributed double value with mean 0.0 and standard deviation 1.0.Exception :NA

The following example shows the usage of java.util.Random.nextGaussian():

**Code –**

`// Java code to demonstrate the working` `// of nextGaussian()` `import` `java.util.*;` ` ` `public` `class` `NextGaussian {` ` ` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` ` ` `// create random object` ` ` `Random ran = ` `new` `Random();` ` ` ` ` `// generating integer` ` ` `double` `nxt = ran.nextGaussian();` ` ` ` ` `// Printing the random Number` ` ` `System.out.println(` `"The next Gaussian value generated is : "` `+ nxt);` ` ` `}` `}` |

**Output –**

The next Gaussian value generated is : -0.24283691098606316

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