Question

Statistical Abstracts (117th edition) provides information about state per capita income taxes. The distribution is mound-shaped with a mean of $1,700 and a a standard deviation of $500.

a. Use the empirical rule and Excel to find an interval centered about the mean in which about 68% of the data will fall.

b. Estimate the range of values centered about the mean in which about 95% of the state per capita income taxes will fall. (Recall the empirical rule )

Answer 1

The empirical rule is the 68 - 95 - 99.7 rule which states that,

(i) The mean divided the bottom 50% from the top 50%

(ii) 68% of the values fall between 1 standard deviation below the mean to 1 standard deviation above the mean.

(iii) 9% of the values fall between 2 standard deviation below the mean to 2 standard deviation above the mean.

(iv) 99.7% of the values fall between 3 standard deviation below the mean to 3 standard deviation above the mean.

The diagram below, will help.

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(a) 68% of the data will fall between 1 standard deviation above that is (1700 + 500) = 2200 and 1 standard deviation below = 1700 - 500 = 1200. The range is from 2200 to 1700 for 68% of the values.

(b) 95% of the data will fall between 2 standard deviation above that is (1700 + 2 *500) = 2700 and 1 standard deviation below = 1700 - 2 * 500 = 700. The range is from 2700 to 700 for 68% of the values.

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