A beginning bowling league has scores that are normally distributed with a mean score of 187 and a standard deviation of 14. Using the empirical rule, about 99.7 percent of the data values lie between which two values?

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that about 68% of data lies within one standard deviation of the mean, about 95% of data lies within two standard deviations of the mean, and about 99.7% of data lies within three standard deviations of the mean.

In this case, the mean bowling score in the league is 187 and the standard deviation is 14. To find the range of scores in which 99.7% of scores are expected to fall, we need to multiply the standard deviation by three to get 42 and then add and subtract this value from the mean. Therefore, 99.7% of scores are expected to fall in the range of 187-42 to 187+42, which simplifies to 145 to 229.

Therefore, using the empirical rule, we can expect that about 99.7% of the bowling scores in the league lie between 145 and 229. It is important to note that while the empirical rule only provides an approximation, it is useful in providing a rough estimate of the spread of data.

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