Question 8

The range is from 28 to 52.

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Given a mean of 40 and a standard deviation of 6, this range is calculated as 40 - 2(6) to 40 + 2(6), resulting in a range from 28 to 52.

A) The range is from 28 to 52.

This option is correct because it accurately reflects the calculation for the range containing approximately 95% of the data in a normal distribution. By taking the mean (40) and subtracting and adding twice the standard deviation (2 * 6 = 12), we get 40 - 12 = 28 and 40 + 12 = 52.

B) The range is from 34 to 46.

This option is incorrect as it does not encompass the full range of approximately 95% of the data. The range from 34 to 46 represents only one standard deviation from the mean (40) and thus covers only about 68% of the data, not the required 95%.

C) The range is from 22 to 58.

This option is also incorrect. While it extends beyond two standard deviations on both sides, the calculated range for 95% of the data should be precisely from 28 to 52. Therefore, this range is too broad and includes data points that fall outside the 95% interval.

D) The range is from 30 to 50.

This option is incorrect as well. The range from 30 to 50 only covers a part of the distribution and reflects slightly less than two standard deviations from the mean. As such, it does not accurately represent the range that includes approximately 95% of the data.

Conclusion

The correct answer, A, is definitive because it follows the statistical rule for normal distributions regarding the spread of data within two standard deviations from the mean. All other options fail to provide the accurate range needed to encompass approximately 95% of the data, highlighting the importance of understanding standard deviation in the context of normal distributions.