Using only the empircal rule use 689599 find the following a

Using only the empircal rule (use .68,.95,.99) find the following:

a) The area between -3 and +2 standard deviations. b) the area between 2 and 1 standard deviations above the mean. c) what percentile lives at 2 standard deviations above the mean? d) the area between the mean and 3 standard deviations below the mean.

Solution

Using only the empircal rule (use .68,.95,.99) find the following:

area between -3 SD and +3 SD = 0.99

area between -3 SD and mean or      mean and +3SD= 0.99/2 =0.495

area between -2 SD and +2 SD = 0.95

area between -2 SD and mean      or    mean and +2SD = 0.95/2=0.475

area between -1 SD and +1 SD = 0.68

area between -1 SD and mean or    mean and +1SD = 0.68/2 = 0.34

=0.495+0.475 =0.97

=0.475-0.34 =0.135

   =area above 2SD = ( 1-0.95)/2 = 0.025

Percentage = 2.5%

d) the area between the mean and 3 standard deviations below the mean.

area between -3 SD and mean = 0.99/2 =0.495