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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