Question

When Aubree goes bowling, her scores are normally distributed with a mean of 190 and a standard deviation of 14. Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?

Answer 1

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

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 = 190

Standard deviation = 14

Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?

148 = 190 - 3*14

So 148 is 3 standard deviations below the mean.

232 = 190 + 3*14

So 232 is 3 standard deviations above the mean

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232