Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 17. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 83 and 117​? ​

(b) What percentage of people has an IQ score less than 49 or greater than 151​? ​

(c) What percentage of people has an IQ score greater than 117​?

Answer 1

According to the empirical rule, 68%, 95% and 99.7% of data values lie within 1, 2 and 3 standard deviations of mean (as illustrated in the figure below).

a) Percentage of people that has an IQ score between 83 and 117​ = 68%

b) Percentage of people has an IQ score less than 49 or greater than 151 = 0.15 + 0.15

= 0.3%

c) Percentage of people has an IQ score greater than 117 = 13.5% + 2.35% + 0.15%

= 16%