Ask Question
30 April, 03:53

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?

+3
Answers (1)
  1. 30 April, 04:10
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers