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IQ Tests and Standard Deviation

Date: 7/28/96 at 9:2:16
From: Anonymous
Subject: Number of Standard Deviations

On standard IQ tests, the mean is 100, with a standard deviation of 
15. The results come very close to fitting a normal curve. Suppose an 
IQ test is given to a very large group of people. Find the percent of 
people whose IQ scores fall into the following categories:

1) greater than 115

2) more than 145

Date: 7/31/96 at 14:34:52
From: Doctor Robert
Subject: Re: Number of Standard Deviations

First, you must convert your scores to z-scores.  A z-score is the 
number of standard deviations that a particular score lies above 
(positive z) or below (negative z) the mean.  For your examples, the 
z-score for 115 is

   z = (115-100)/15  = 1.

You then go to a z-table which tells you that 84.13 percent of the 
scores in a normal population lie below z = 1.  Therefore, there must 
be 100-84.13 = 15.87 percent of the population having IQ's above 115.

The z-score for 145 is z = (145-100)/15 = 3.  From the tables, 99.87 
percent of the population lie below z = 3.  Therefore, .13 percent of 
the population have IQs greater than 145. A z-table can be found in 
the back of almost any statistics book.

-Doctor Robert,  The Math Forum
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Associated Topics:
High School Statistics

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