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The mean monthly mortgage paid by all home owners in a city is $1320 with a standard deviation of $105. Using Chebyshev's theorem, find the interval, [L,U] , that contains monthly mortgage payments of at least 75% of all homeowners. Round your answers to two decimal places.

Respuesta :

Using Chebyshev's Theorem, it is found that the interval that contains monthly mortgage payments of at least 75% of all homeowners is [1110, 1530].

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.

In this problem:

  • The mean is of $1320.
  • The standard deviation is of $105.

By the Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean, hence:

  • [tex]1320 - 2(105) = 1110[/tex]
  • [tex]1320 + 2(105) = 1530[/tex]

The interval that contains monthly mortgage payments of at least 75% of all homeowners is [1110, 1530].

To learn more about the Chebyshev's Theorem, you can take a look at https://brainly.com/question/25303620

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