NORMAL DISTRIBUTIONNormal distribution is a continuous distribution having the following properties:1. Its probability curve is bell-shaped.2. Its mean, mode, and median are equal and located at the centre of the distribution. 3. It is a unimodal distribution.4. The curve is symmetrical about the mean. Thus it has same shape on both sides of a vertical line drawn through the centre.5.The curve never touches the horizontal axis or mathematically it touches at infinity. 6. The total area under the curve is equal to 1.0.7. The area under the normal curve that lies within one standard deviation of the mean is 0.68 (or 68%); within two standard deviations of the mean is 0.95 (or 95%); within three standard deviations of the mean is 0.997 (or 99.7%). See Figure 8.18. The normal distribution has two parameters known as its mean and variance 2 .9.Continuous random variable X from normal distribution with mean and variance 2 is denoted by X N( ,2 ).

Standard Normal DistributionLet X be a continuous random variable from a normal distribution N(, 2), then X can be transformed to Z score of standard normal distribution by the following Formula: