Standard Normal Distribution
A standard normal distribution is a normal distribution with mean 0, standard deviation 1, Area under curve 1 and of infinite extent. When the unit of measure is changed to measure standard deviations from the mean, thenall normal distributions will become equivalent to the standard normal distribution. Transformation of Normal distributions into standard normal distribution is given by the formula:
where X -a score, μ -the mean, σ – the standard deviation of original normal distribution. The standard normal distribution is oftenknown as the z distribution.A z score tells us how far the score is from the mean in terms of number of standard deviations. Percentile rankis the area (probability) to the left of the value i.e.,by adding the percentages from the chart from left of the curve.The mean is the 50th percentile (50%).
From the 68-95-99.7 rule/Empirical rule:
For a variable with the standard normal distribution,
- 68% of the observations fall between -1 and 1 (within 1 standard deviation of the mean of 0),
- 95% fall between -2 and 2 (within 2 standard deviations of the mean) and
- 7% fall between -3 and 3 (within 3 standard deviations of the mean).
