Question

When Gabriella goes bowling, her scores are normally distributed with a mean of 170

and a standard deviation of 13. Using the empirical rule, determine the interval that


would represent the middle 95% of the scores of all the games that Gabriella bowls.

Answer 1

The interval that would represent the middle 95% of the scores of all the games that Gabriella bowls is from 144 to 196.

Explanation:

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

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

95% of the measures are within 2 standard deviation of the mean.

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

In this problem, we have that:

Mean = 170

Standard deviation = 13

Middle 95% of the scores.

Within 2 standard deviations of the mean.

170 - 2*13 = 144

170 + 2*13 = 196

The interval that would represent the middle 95% of the scores of all the games that Gabriella bowls is from 144 to 196.