Based on these facts, would you expect batting averages above .350 to be more or less common today than in the past? A. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation is lower, thus it is less probable to have such a high batting average. B. Because the mean is unchanged, batting averages above .350 are more common today because the standard deviation is higher, thus it is less probable to have such a high batting average. C. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation is higher, thus it is more probable to have such a high batting average. D. Because the mean is unchanged, batting averages above 350 are more common today because the standard deviation is lower, thus it is less probable to have such a high batting average.

To analyze the question regarding batting averages above .350, we need to consider the relationship between the mean, standard deviation, and the distribution of batting averages. 1. **Mean**: The average batting average remains unchanged. 2. **Standard Deviation**: This measures the spread of the batting averages around the mean. Now, let's evaluate the options: - **Option A**: This states that batting averages above .350 are less common today because the standard deviation is lower. This is correct because a lower standard deviation means that the data points (batting averages) are closer to the mean, making it less likely to have values significantly above the mean, such as .350. - **Option B**: This suggests that batting averages above .350 are more common today because the standard deviation is higher. This is incorrect because a higher standard deviation would mean a wider spread of values, but since the mean is unchanged, it does not imply that values above .350 are more common. - **Option C**: This states that batting averages above .350 are less common today because the standard deviation is higher. This is contradictory because a higher standard deviation would actually allow for more values above the mean, making it more likely to have high averages. - **Option D**: This suggests that batting averages above .350 are more common today because the standard deviation is lower. This is incorrect for the same reason as option A; a lower standard deviation would make high averages less common. Based on this analysis, the correct answer is: **A. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation is lower, thus it is less probable to have such a high batting average.**