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%**

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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
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