Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 19. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 62 and 138​? ​(b) What percentage of people has an IQ score less than 43 or greater than 157​? ​(c) What percentage of people has an IQ score greater than 138​? ​(a) 95​% ​(Type an integer or a​ decimal.)

Answer 1

= 100, = 19

According to empirical rule,

Approx. 68% of the data lies between ± 1 Standard deviation, or between 81 and 119

Approx. 95% of the data lies between ± 2 Standard deviation, or between 62 and 138

Approx. 99.7% of the data lies between ± 3 Standard deviation, or between 43 and 157

a)

IQ score between 62 and 138 lie within ± 2 Standard deviation, hence

percentage of people has an IQ score between 62 and 138​= 95 %

b)

IQ score between 43 and 157 lie within ± 3 Standard deviation, hence 99.7 % of people has an IQ score between 62 and 138​.

percentage of people has an IQ score less than 43 or greater than 157 = 1 - 99.7

percentage of people has an IQ score less than 43 or greater than 157 = 0.30%

c)

percentage of people has an IQ score greater than 138​ = 2.35% + 0.15% = 2.50%

percentage of people has an IQ score greater than 138​ = 2.50%