Normal Distribution Worksheet

This worksheet help you to understand 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 if the probability function is given by normal distribution formula

The constants of normal distribution is
1. Mean = ג (Lamda)
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 = μ
5. Symmetrical about the ordinate X = μ and hence skewness is zero
6. The normal curve has points of inflections at X = μ + σ & X = μ - σ


ExampleCalculate 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 such calculations on your own, this normal distribution calculator can be used to verify the results of your calculations.