Normal Distribution Worksheet

This worksheet may help you to know about the Normal (or) Gaussian Distribution. A continuous random variable X is said to follow normal distribution with mean and Standard deviation σ if the probability function is given by

Normal Distribution Formula

Normal Distribution Formula
Normal or Gaussian Distribution Calculator is used to calculate the normal probability density function for a given mean and standard deviation. 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 = mu
  5. Symmentrical 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

Normal Distribution Example

Calculate Gaussian Distribution for Mean = 50, S.D. = 8, X1= 34,X2= 62.
Z = (X - )/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

The above worksheet is a walk through to understand the concept of Normal Distribution when it comes to online calculation this Normal Distribution Calculator is an essential tool to make the calculation easy.


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