Question

The mean score on a driving exam for a group of driver's education students is 84 points, with a standard deviation of 4 points. Apply Chebycher's Theorem to the data using k =2. Interpret the results.
At least % of the exam scores fall between and
(Simplify your answers.)

Answer 1

Using Chebyshev's Theorem, it is found that:

At least 75% of the exam scores fall between 76 and 92.

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• Chebyshev's Theorem states that the percentage of measures within k standard deviations of the mean is of at least $100(1 - \frac{1}{k^{2}})$.

• With k = 2, that is, within 2 standard deviations of the mean:

$P = 100(1 - \frac{1}{2^{2}})$

$P = 100(1 - \frac{1}{4})$

$P = 100(\frac{3}{4})$

$P = 75$

• At least 75% of the measures are within 2 standard deviations of the mean.

84 - 2(4) = 76

84 + 2(4) = 92

• Thus, at least 75% of scores between 76 and 92.

A similar problem is given at brainly.com/question/23612895