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?
(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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