From the information found in the Statistical Abstract of th

From the information found in the Statistical Abstract of the United States (117th edition) it was determined that the median income for households in each of the fifty states, in thousands of dollars, has mean = 33.81 and standard deviation = 5.10.

(a) Use Chebyshev\'s Theorem to find an interval in which at least 75% of the states\' median incomes will lie.

(b) Use Chebyshev\'s Theorem to find an interval in which at least 93.8% of the states\' median income will lie.

Solution

Step 1: Square the number of standard deviations:
2^2 = 4.

Step 2: Divide 1 by your answer to Step 1:
1 / 4 = 0.25.

Step 3: Subtract Step 2 from 1:
1 – 0.25 = 0.75.

At least 75% of the observations fall between -2 and +2 standard deviations from the mean.
That’s:
mean – 2 standard deviations
33.81 – 5.1(2) =23.61
mean + 2 standard deviations
33.81 + 5.1(2) =44.01
Between 23.61 and 44.01 Answer