IQ scores have an approximately bell-shaped distribution with mean 100 and standard deviation 15. Use the Empirical Rule to answer the following questions.

Question

What percentage of IQ scores are above 130?

What percentage of IQ scores are below 115?

What percentage of IQ scores are between 70 and 85?

Answer 1

2.5% above 130; (100-95)/2 = 2.5

84% below 115; 100-(100-68)/2 = 84

70 to 85 is (100-68)/2 - (100-95)/2 = 16-2.5 = 13.5%

it may help to draw a bell shaped curve with vertical lines though it at 0, 1 and 2 standard deviations from the mean and calculate the areas between the lines. it's 2.5 - 13.5 - 34 - 34 - 13.5 - 2.5 percents total areas under the curve sums to 100%. the middle 34+34 = 68%, the middle 4 areas 13.5+34+34+13.5 = 95%

empirical rule is 68-95-99.7 % for 1, 2 and 3 standard deviations from the mean.

Answer 2

130 is 2 standard deviations above the mean. Per the empirical rule 2.4% of the scores would be more than 2 standard deviations above the mean.

115 is 1 standard deviation above the mean. Per the empirical rule 84% of the score would be less than 1 standard deviation below the mean.

70 is 2 standard deviations below the mean and 85 is 1 standard deviation below the mean. Per the empirical rule 13.5% of the scores would be between 2 standard deviations below the mean and 1 standard deviation below the mean.