Question

Scores of an IQ test have a bell-shaped distribution with a meanhof 100 and a standard deviation of 13 . Use the empirical rule to determine the following.

What percentage of people has an IQ score between 61 and 139 ?

Answer 1

To determine the percentage of people with an IQ score between 61 and 139, we can use the empirical rule. The percentage is approximately 99.7%.

Step-by-step explanation:

To use the empirical rule to determine the percentage of people with an IQ score between 61 and 139, we need to calculate the z-scores for these values. The z-score formula is (X - mean) / standard deviation, where X is the IQ score.

For an IQ score of 61, the z-score is (61 - 100) / 13 = -3. When the z-score is -3, the percentage of people below that score is 0.15%. So, the percentage of people with an IQ score less than 61 is 0.15%.

For an IQ score of 139, the z-score is (139 - 100) / 13 = 3. When the z-score is 3, the percentage of people below that score is 99.85%. So, the percentage of people with an IQ score less than 139 is 99.85%.

To find the percentage of people with an IQ score between 61 and 139, we subtract the percentage below 61 from the percentage below 139: 99.85% - 0.15% = 99.7%.