Answer
a. k=1 we can not use the theorem for this case.
b. 12.5% of data will be more than 80,900 dollars.
c. 3.7% of the data will be more than 100,000 dollars.
Work Step by Step
Chebyshev’s theorem: The proportion of values from a data set that will fall within k standard deviations of the mean will be at least $1−1/k^2$ where k is a number greater than 1.
μ=58500 and σ=11200
a. This range is within 1σ. The Chebyshev’s theorem requires that k>1 and we can not use the theorem for this case.
b. This position is at 2σ to the right of the mean. The Chebyshev’s theorem indicates that 1−1/4=0.75 fall within 2σ and the percentage to the right would be (1−0.75)/2=0.125, which means 12.5% of data will be more than 80,900 dollars.
c. This position is about 3.7σ to the right of the mean, the Chebyshev’s theorem gives $1−1/3.7^2=0.927$ or 92.7% within and (1−0.927)/2=0.037 or 3.7% of the data will be more than 100,000 dollars.
