Question

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

100

and a standard deviation of

16.

Use the empirical rule to determine the following.

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

68

and

132?

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

52

or greater than

148?

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

132?

Answer #1

(a)

= 100

= 16

To find P(68 <X < 132):

Case 1:For X from 68 to mid value:

Z = (68 - 100)/16

= - 2

Case 2: For X from mid value to 132:

Z = (132 - 100)/16

=2

By Empirical Rule, 95% of data points lie between 2 Standard deviations from mean.

So,

Answer is:

**95%**

(b)

To find P(X<52 OR X>148):

Case 1: For X < 52

Z =(52 - 100)/16

= - 3

Case 2: For X > 148

Z = (148 - 100)/16

= 3

By Empirical Rule, 99.7% of data points lie within 3 Standard Deviations from mean.

So,

Percentage outside 3 Standard Deviations from mean.= 100 - 99.7 = 0.3%

So,

Answer is:

**0.3%**

(c)

To find P(X >132):

Z= (132 - 100)/16

= 2

By Empirical Rue, 95% of data points lie between 2 Standard deviations from mean..

So,

Percentage from mid value to 2 SD on RHS = 95%/2 = 47.5%

So,

P(X>132)= 50% - 47.5% = 2.5%

So,

Answer is:

**2.5%**

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Use the empirical rule to determine the following. (In the
answer do not write the % symbol).
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148?
%
(b) What percentage of people have an IQ score less than 84 or
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148? %
(d)...

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mean of 100 and a standard deviation of 16 . Use the empirical rule
to determine the following.
(a) What percentage of people has an IQ score between 52 and
148 ?
(b) What percentage of people has an IQ score less than 84 or
greater than 116 ?
(c) What percentage of people has an IQ score greater than 116
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160?
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and a standard deviation of
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Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between
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