If is the mean and sigma is the Standard Deviation of a set

If is the mean and sigma is the Standard Deviation of a set of measurements which are normally distributed, what percentage of the data is...

Solution

a) about 95%

b) 1 - 0.95 = 5%

c) 1 - (0.05/2) = 0.975 = 97.5%

d) inside +/-3 sigma we have 99.7% => outside +/- 3 sigma we have (1-0.997) => on right tail we have (1-0.997)/2 => less than 3 sigma we have 1 - (1-0.997)/2 = 0.9985