Question

A random sample of 25 U.S. residents was selected using census data from the year 2000. The dotplot below shows the distribution of total personal income (in thousands) for the members of the sample. The mean of this distribution is $25,615 and the standard deviation is $25,333.What percent of the sample had total personal incomes within two standard deviations of the mean?

Answer 1

95%

Explanation:

Data falls within 2 standard deviations from the mean - is calculated using;

μ – 2σ and μ + 2σ .

The mean of this distribution is $25,615 and the standard deviation is $25,333.

μ – 2σ

= $25,615 - 2($25,333)

=$-25051

μ + 2σ

= $25,615 + 2($25,333)

= 76,281

Empirical rule states that: 95% of data falls within 2 standard deviations from the mean

Hence, 95% the sample had total personal incomes within two standard deviations of the mean.