Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following. What percentage of people has an IQ score between 76 and 124​?

Answer 1

The percentage of people with an IQ score between 76 and 124 is approximately 95%.

Step-by-step explanation:

To find the percentage of people with an IQ score between 76 and 124, we can use the empirical rule for a bell-shaped distribution. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and more than 99% falls within three standard deviations.

Since the mean IQ score is 100 and the standard deviation is 12, we can calculate the distance from the mean to each boundary of the range:

Lower boundary: 76 - 100 = -24

Upper boundary: 124 - 100 = 24

The range of 76 to 124 falls within two standard deviations of the mean, so we can apply the empirical rule.

Therefore, the percentage of people with an IQ score between 76 and 124 is approximately 95%.