Answer:
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).