Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of

100

and a standard deviation of

12

Use the empirical rule to determine the following.​(a) What percentage of people has an IQ score between

64

and

136?

​(b) What percentage of people has an IQ score less than

88

or greater than

112​?

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

136​?

Answer 1

Solution :

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

(a)

P( - 3< X < + 3) = 99.7%

P(100 - 3* 12 < X < 100 + 3 * 12) = 99.7%

P(64 < X < 136) = 99.7%

99.7%

(b)

P(X < 88) = 16%

(c)

P(X > 136) = 0.3%