Question

It is often assumed that IQ scores follow a bell-shaped distribution with a mean of 100 and a standard deviation of 16 .

a. Approximately what percentage of scores are between 84 and 116 ?
b. Approximately what percentage of scores are less than 68 ?
c. Approximately what percentage of scores are more than 116 ?

Answer 1

In a normal distribution of IQ scores with a mean of 100 and a standard deviation of 15, about 68% of people have scores between 84 and 116, around 2.2% have scores less than 68, and approximately 32% have scores above 116.

Step-by-step explanation:

The question pertains to the properties of a normal distribution of IQ scores, which is a topic in statistics, a branch of mathematics. When considering a normal distribution with a mean of 100 and a standard deviation of 15:

• a. Approximately 68% of scores are between 84 (one standard deviation below the mean) and 116 (one standard deviation above the mean), due to the empirical rule.
• b. Approximately 2.2% of scores are less than 68 (two standard deviations below the mean).
• c. More than 116 corresponds to the upper tail of the distribution which captures all scores above one standard deviation of the mean. Since 68% fall within one SD and 95% within two SDs, subtracting 68% from 100% gives approximately 32% of scores that are more than 116 points.