# Question

Consider the following sample of exam scores, arranged in increasing order.

The sample mean and sample standard deviation of these exam scores are, respectively, 85 and 16.1.

a. Use Chebychev’s rule to obtain a lower bound on the percentage of observations that lie within two standard deviations to either side of the mean.

b. Use the data to obtain the exact percentage of observations that lie within two standard deviations to either side of the mean. Compare your answer here to that in part (a).

c. Use Chebychev’s rule to obtain a lower bound on the percentage of observations that lie within three standard deviations to either side of the mean.

d. Use the data to obtain the exact percentage of observations that lie within three standard deviations to either side of the mean. Compare your answer here to that in part (c).

The sample mean and sample standard deviation of these exam scores are, respectively, 85 and 16.1.

a. Use Chebychev’s rule to obtain a lower bound on the percentage of observations that lie within two standard deviations to either side of the mean.

b. Use the data to obtain the exact percentage of observations that lie within two standard deviations to either side of the mean. Compare your answer here to that in part (a).

c. Use Chebychev’s rule to obtain a lower bound on the percentage of observations that lie within three standard deviations to either side of the mean.

d. Use the data to obtain the exact percentage of observations that lie within three standard deviations to either side of the mean. Compare your answer here to that in part (c).

## Answer to relevant Questions

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