Question

Jan 25,10:31:53AM 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

To determine the interval that represents the middle 68% of Riley's bowling scores using the empirical rule (also known as the 68-95-99.7 rule for a normal distribution), you can use the following guidelines:

1. The middle 68% of scores falls within one standard deviation of the mean (i.e., 68% of scores fall between the mean minus one standard deviation and the mean plus one standard deviation).

Given:

- Mean (μ) = 160

- Standard Deviation (σ) = 13

You can calculate the interval as follows:

Lower Bound = Mean - 1 * Standard Deviation

Lower Bound = 160 - 1 * 13

Lower Bound = 160 - 13

Lower Bound = 147

Upper Bound = Mean + 1 * Standard Deviation

Upper Bound = 160 + 1 * 13

Upper Bound = 160 + 13

Upper Bound = 173

So, the interval that represents the middle 68% of Riley's bowling scores is from 147 to 173.

Explanation: