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The mean score on a driving exam for a group of​ driver's education students is 84 ​points, with a standard deviation of 6 points. Apply​ Chebychev's Theorem to the data using k=2. Interpret the results.

At least _% of the exam scores fall between _ and _.
Simplify your answers.

Sagot :

Answer:

At least 75% of the exam scores fall between 72 and 96.

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 [tex]100(1 - \frac{1}{k^{2}})[/tex].

Apply​ Chebychev's Theorem to the data using k=2.

k = 2, so within 2 standard deviations of the mean, interval in which at least 75% of the measures fall.

In this question:

Mean of 84, standard deviation of 6.

84 - 2*6 = 84 - 12 = 72

84 + 2*6 = 84 + 12 = 96

At least 75% of the exam scores fall between 72 and 96.

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