Suppose that quiz scores in a beginning statistics class have a mean of 7.0 with a standard deviation of 0.6. Using Chebyshev's Theorem, what is the minimum percentage of quiz scores between 5.8 and 8.2

The minimum percentage of quiz scores between 5.8 and 8.2 is 75%.

Step-by-step 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 .

In this question:

The mean is 7, and the standard deviation is 0.6.

What is the minimum percentage of quiz scores between 5.8 and 8.2?

7 - 2*0.6 = 5.8

7 + 2*0.6 = 8.2

Within 2 standard deviations of the mean, so, by the Chebyshev Theorem:

The minimum percentage of quiz scores between 5.8 and 8.2 is 75%.

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step-by-step explanation:

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