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University students in an Iowa town have a mean hourly wage of $11.75, with a standard deviation of $1.25. 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?

Round your answers to the nearest hundredth.

Sagot :

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.

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 [tex]100(1 - \frac{1}{k^{2}})[/tex].

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:

  • 11.75 - 2 x 1.25 = $9.25.
  • 11.75 + 2 x 1.25 = $14.25.

More can be learned about the Chebyshev Theorem at https://brainly.com/question/25303620

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