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26 September, 00:53

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution cannot be regarded as bell-shaped. What can be said about the percentage of salaries that are less than $68,000 or more than or more than $92,000? choices belowa. It is at least 75 percent. b. It is at least 55 percent. c. It is at least 25 percent. d. It is at most 25 percent.

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  1. 26 September, 04:51
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    d. It is at most 25 percent.

    Step-by-step explanation:

    When the distribution is not normal, we use the Chebyshev's theorem, which 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, we have that:

    Mean = 80,000

    Standard deviation = 6,000

    What can be said about the percentage of salaries that are less than $68,000 or more than or more than $92,000?

    68000 = 80000 - 2*6000

    So 68000 is two standard deviations below the mean

    92000 = 80000 + 2*6000

    So 92000 is two standard deviations above the mean.

    By Chebyshev's Theorem, at least 75% of the salaries are between $68,000 and $92,000. Others, which are at most 25%, are either less than $68,000 or more than $92,000.

    So the correct answer is:

    d. It is at most 25 percent.
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