The distribution of the IQ Intelligence Quotient is approxim

The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, only 0.15% of people have an IQ over what score?

Solution

Given mean =100 and standard deviation =15

from the standard deviation rule, 99.73% observations fall with in 3 standard deviations of the mean

and 99.7% observations fall with in 2.97 standard deviations of the mean; This means 0.15% of the observations ar e the above 3 standard deviations of the mean

Therefore , mean + 2.7SD = 100+ 2.7*15 =144.51

The people have an IQ of 145 or above are 0.15%