Question

People in a town have a mean hourly wage of $13.69, with a standard deviation of $4.77. The distribution of hourly wages is not assumed to be symmetric. Between what two-hourly wages does Chebyshev's Theorem guarantee that we will find at least 75% of the people?

Answer 1

Using Chebyshev's Theorem, we are guaranteed to find at least 75% of the people earning hourly wages between $4.15 and $23.23.

What does Chebyshev’s Theorem state?

When the distribution is not normal, Chebyshev's Theorem is used. 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 $100(1 - \frac{1}{k^{2}})$.

In this problem, we want the values within 2 standard deviations of the mean, hence the values are:

• 13.69 - 2 x 4.77 = $4.15.

• 13.69 + 2 x 4.77 = $23.23.

More can be learned about Chebyshev's Theorem at brainly.com/question/25303620

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