Question

When Riley goes bowling, her scores are normally distributed with a mean of 160 and

a standard deviation of 13. Using the empirical rule, determine the interval that
would represent the middle 68% of the scores of all the games that Riley bowls.

Answer 1

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 160, standard deviation of 13.

Middle 68% of the scores of all the games that Riley bowls.

Within 1 standard deviation of the mean, so:

160 - 13 = 147.

160 + 13 = 173.

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).