Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Using the empirical rule, determine the interval that would represent the middle 99. 7% of IQ scores

Answer 1

The interval that would represent the middle 99.7% of IQ scores is (55, 145).

Explanation:

The empirical rule tells us that 68% of values are within one standard deviation from the mean, 95% of values are within two standard deviations from the mean, and 99.7% of values are within three standard deviations from the mean.

If we want to determine the interval representing the middle 99.7% of IQ scores, we need to determine the values that are three standard deviations from the mean.

We are given the standard deviation of 15 and a mean of 100. Three standard deviations from the mean can be calculated as such:

• 100 - 15(3) < 100 < 100 + 15(3)
• 100 - 45 < 100 < 100 + 45
• 55 < 100 < 145

The interval that represents the middle 99.7% of IQ scores is (55, 145).