Question

when travis goes bowling, his scores are normally distributed with a mean of 145 and a standard deviation of 12. using the empirical rule, what percentage of the games that travis bowls does he score between 109 and 181?

Explanation:

Step1: Find how many standard deviations 109 and 181 are from the mean.

The mean ($\mu$) is 145 and the standard deviation ($\sigma$) is 12.
For 109: $z=\frac{109 - 145}{12}=\frac{- 36}{12}=- 3$
For 181: $z=\frac{181 - 145}{12}=\frac{36}{12}=3$

Step2: Apply the empirical rule.

The empirical rule states that for a normal distribution, about 99.7% of the data lies within 3 standard deviations ($\mu\pm3\sigma$) of the mean. Since 109 is $\mu - 3\sigma$ and 181 is $\mu+3\sigma$, the percentage of data between them is 99.7%.

Answer:

99.7%