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 = σ^{2}

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

__Example__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 = Z_{1} (say)

When X = 62

Z = (62 - 50)/8

= 1.5 = Z2 (say)

Therefore,

P(34 < X < 62) = P(Z_{1} < X < Z_{2})

= 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.

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