Question

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

Answer 1

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

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
`100(1 - (1)/(k^(2)))`.

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%.