Answer:
About 99.7% of the IQ scores would be between 57 and 141.
Step-by-step explanation:
The Empirical Rule about a bell-shaped curve states that :
- 68% of the data lies within one standard deviation of the mean (both left-side and right-side)
- 95% of the data lies within two standard deviations of the mean (both left-side and right-side)
- 99.7% of the data lies within three standard deviations of the mean (both left-side and right-side)
Now, we need to find what percentage of IQ scores lies between 57 and 141 : Mean = 99 and standard deviation = 14
141 – 99 = 42
= 3 × 14
Thus, 141 is 3 standard deviations to the right of the mean.
99 – 57 = 42
= 3 × 14
Thus, 57 is 3 standard deviations to the left of the mean.
Since 57 to 141 is within 3 standard deviations of the mean, and according to empirical formula stated above : about 99.7% of the IQ scores would be between 57 and 141.
