Question

Scores of an IQ test have a bell-shapped distribution with a mean of 100 and standard deviation of 15. Use the empirical rule to determine the following.

A.) What percentage of people has an IQ between 55 and 145?

B.) What percentage of people has an IQ score less than 85 or greater than 115?

C.) What percentage of people has an IQ score greater than 145?

(Type an integer or decimal.)

Answer 1

= 100 and = 15

Using the z score to calculate

A) Percentage of people with an 55<IQ<145

z at IQ=55

z at IQ = 145

Using the z table,

Area(-3<z<3) = 0.99865-0.00135= 99.73%

B) Percentage of people with an IQ<85 or IQ>115

z at IQ=85

z at IQ = 115

Using the z table,

Area(z<-1 or z>1) = 0.15866 + (1-0.84134) = 31.73%

C) Percentage of people with an IQ>145

z at IQ = 145

Using the z table,

Area(z>3) =1-0.99865= 0.13%