Question

An IQ test produces scores that are normally distributed with a mean value of 100 and a standard deviation of 14.2. What is the range of the top 1 percent of all scores?

Answer 1

To find the range of the top 1 percent of IQ scores, a Z-score that signifies the top 1 percent on the standard normal distribution is identified and then scaled to the IQ test's distribution by multiplying it by the standard deviation and adding the mean, resulting in an IQ score of around 133 or higher for the top 1 percent.

Step-by-step explanation:

The question asks about the range of the top 1 percent of IQ scores when the IQ scores follow a normal distribution with a mean of 100 and standard deviation of 14.2. To find this range, one would use a Z-score table to identify the Z-score that corresponds to the top 1 percent of a normal distribution, which is approximately 2.33. This Z-score then needs to be scaled to the specific IQ test's distribution.

To do this, we multiply the Z-score by the standard deviation and then add the mean. The calculation would be:

• Z-score (2.33) × Standard Deviation (14.2) = 33.066
• Mean (100) + 33.066 = 133.066

This means that to be in the top 1 percent of IQ scores, a score would typically need to be around 133 or higher on this IQ test. Keep in mind that individual IQ tests may vary slightly due to their specific scaling and norming procedures.