Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 99 and a standard deviation of 14. Using the empirical rule, what percentage of IQ scores are between 57 and 141?

Answer 1

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.