About 95 of the values lie within two standard deviations. Normal Distribution Z 1459 120 17. The equation for the standard normal distribution is.
This fact is known as the 68-95-997 empirical rule or the 3-sigma rule.
For Georges example we need to use the 2nd table as his test result. By the formula of the probability density of normal distribution we can write. When a distribution is normal then 68 of it lies within 1 standard deviation 95 lies within 2 standard deviations and 99 lies with 3 standard deviations. Thats where z-table ie.