# 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 distribution
X = value on the original distribution
u = mean of the original distribution
s = 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 :
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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