Probability Distribution – Normal: The Normal probability distribution also known as Gaussian distribution, is a probability distribution that is symmetric about mean with data tends to lie near mean and frequency of occurrence decreases as we move away from mean.
The Bell shaped Curve:
The Normal distribution is also known as “Bell Shaped curve” with data equally distributed on the both side of the mean. Since data is equally distributed above and below mean, so for normal distribution Mean Median and mode are equal.
The Normal Distribution Function:
Properties of Normal Distribution:
- The Normal Distribution can completely be described by mean and variance(standard distribution)
- Skewness of normal distribution is equal to zero
- Kurtosis for normal distribution is equal to 3
- A linear combination of normally distributed independent random variable is also normally distributed
- The probabilities of outcomes further above and below the mean get smaller and smaller but do not go to zero (Asymptotic)
Standard Normal Distribution: A standard normal distribution (i.e., Z-distribution) is a normal distribution that has been standardized so it has a mean of zero and a standard deviation of 1.
The Standard normal distribution is also known as Z- Distribution which gives the number standard deviation a given data point lie away from mean. The Standard Normal Distribution has the following formula.