Normal Distribution Tutorial

Normal Distribution Tutorial

Definition:

The Normal Distribution is also called the Gaussian distribution. It is defined by two parameters mean ('average' m) and standard deviation (σ). A theoretical frequency distribution for a set of variable data, usually represented by a bell-shaped curve symmetrical about the mean.

Formula:

X < mean = 0.5-Z X > mean = 0.5+Z X = mean = 0.5 Z = (X-m) / σ
where,

m = Mean. σ = Standard Deviation. X = Normal Random Variable

Example:

If X is a normal random variable with mean (m) 100 and standard deviation (σ) 6 find P(X<106)

Step 1:

For a given value X=106 Z = (106-100)/6 = 1

Step 2:

Find the value of 1 in Z table Z = 1 = 0.3413

Step 3:

Here the X value is greater than mean P(X) = 0.5 + 0.3413 = 0.8413

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