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# Standard Normal Distribution (SND) – Java Program

• Last Updated : 06 Feb, 2018

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 distribution
X = value on the original distribution
u = mean of the original distribution
s = standard deviation of the original distribution
```

Code –

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 `// 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 :
NA
Return 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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