Question

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

100

and a standard deviation of

20.

Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between

80

and

120

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

40

or greater than

160

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

120

Answer 1

Solution :

Given that,

Using Empirical rule,

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

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

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

(a)

P(80< x < 120) = P(x < 120) - P(x < 80) = 0.68 = 68%

(b)

P(x < 40 or x > 160) = 99.7%

(c)

P(x > 120) = 1 - P(x < 120) = 1 - 0.84 = 0.16 = 16%