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A sample of assistant professors on the business faculty at state supported institutions in Ohio revealed the mean income to be $32,000 for 9 months with a standard deviation of $3,000. Using Chebyshev's Theorem, what is the proportion of faculty that earns more than $25,250 but less than $38,750

User Daiwen
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Answer:

The proportion of faculty that earns more than $25,250 but less than $38,750 is 0.8025.

Explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by
100(1 - (1)/(k^(2))).

In this question, we have that:

Mean of 32000, Standard deviation of 3000.

Using Chebyshev's Theorem, what is the proportion of faculty that earns more than $25,250 but less than $38,750

This is within 38,750 - 32,000 = 32,000 - 25,250 = $6,750 of the mean.

Value of k:

This is k standard deviations from the mean. k is given by:


k = (6750)/(3000) = 2.25

Proportion:

The percentage is:


p = 100(1 - (1)/((2.25)^(2))) = 80.25.

So the proportion is 0.8025

User Cary Jensen
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