Use the normal distribution of IQ scores which has a mean of

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

Solution

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%