When Montraie goes bowling, his scores are normally distributed with a mean of 185 and a standard deviation of 14. Using the empirical rule, determine the interval that would represent the middle 99.7% of the scores of all the games that Montraie bowls.
The middle 99.7% of scores lie within 3 standard deviations of the mean in a normal distribution.
So, to find the interval representing the middle 99.7% of scores:
Lower limit = mean - 3 * standard deviation
Lower limit = 185 - 3 * 14
Lower limit = 185 - 42
Lower limit = 143
Upper limit = mean + 3 * standard deviation
Upper limit = 185 + 3 * 14
Upper limit = 185 + 42
Upper limit = 227
Therefore, the interval representing the middle 99.7% of scores of all the games that Montraie bowls is 143 to 227.