Use the normal distribution of IQ scores, which has a mean of 90 and a standard
ID: 3021163 • Letter: U
Question
Use the normal distribution of IQ scores, which has a mean of 90 and a standard deviation of 18, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.
Standard score
Percent
-3.0
0.13
-2.5
0.62
-2
2.28
-1.5
6.68
-1
15.87
-0.9
18.41
-0.5
30.85
-0.1
46.02
0
50.00
0.10
53.98
0.5
69.15
0.9
81.59
1
84.13
1.5
93.32
2
97.72
2.5
99.38
3
99.87
3.5
99.98
A. The percentage of scores between 45 and 135 is _____% (round to two decimal places as neeed.)
Standard score
Percent
-3.0
0.13
-2.5
0.62
-2
2.28
-1.5
6.68
-1
15.87
-0.9
18.41
-0.5
30.85
-0.1
46.02
0
50.00
0.10
53.98
0.5
69.15
0.9
81.59
1
84.13
1.5
93.32
2
97.72
2.5
99.38
3
99.87
3.5
99.98
Explanation / Answer
Use the normal distribution of IQ scores, which has a mean of 90 and a standard deviation of 18, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.
Z score for 45, z=(45-90)/18 =-2.5
From tables, P( z < -2.5) = 0.62%
Z score for 135, z=(135-90)/18 = 2.5
From tables, P( z < 2.5) = 99.38%
P( 45 <x<135)
= P( -2.5 < z < 2.5)
= P( z < 2.5) – P( z < -2.5)
= 99.38 - 0.62
= 98.76
percentage of scores between 45 and 135 is 98.76%
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