Normal Distribution Worksheet

This below worksheet containing the solved example shows how to compute Normal (or) Gaussian Distribution. A continuous random variable X is said to follow normal distribution with mean µ and Standard deviation σ then the probability function given by



The constants of Normal Distribution are
1. Mean = µ
2. Variance = σ²
3. Standard Deviation = σ

Properties of Normal Distribution
1. The normal curve is bell shaped
2. Mean = Median = Mode
3. X - axis is an asymptote to the normal curve
4. Unimodal at X = mu
5. Symmetrical about the ordinate X = mu and hence skewness is zero
6. The normal curve has points of inflections at X = mu + sigma & X = mu - sigma

Solved Example - Normal Distribution
Calculate Gaussian Distribution for Mean = 50, S.D. = 8, X1= 34,X2= 62.
Z = (X - µ)/σ
When X = 34
Z = (34 - 50)/8
= -2 = Z₁ (say)
When X = 62
Z = (62 - 50)/8
= 1.5 = Z2 (say)
Therefore ,
P(34 < X < 62) = P(Z₁ < X < Z₂)
= P(-2 < X < 1.5)
= P(-2 < X < 0) + P(0 < X < 1.5) [calculate equivalent value for Normal distribution PDF table]
= 0.4772 + 0.4332
= 0.9104

When you try yourself such calculations, this Normal Distribution Calculator can be used to verify your results.