15. The scores on a nationally administered standardized test are normally distributed. Which portion of the data is within two standard deviations of the mean?
Answer: C
95% of the data is within two standard deviations of the mean.
In a normal distribution, approximately 95% of the scores fall within two standard deviations of the mean. This is a key concept in statistics known as the empirical rule or the 68-95-99.7 rule.
A) 50%
This option is incorrect as it underestimates the portion of data within two standard deviations. In a normal distribution, 50% of the data lies below the mean, not within two standard deviations.
B) 68%
While 68% of the data is indeed within one standard deviation of the mean, this option does not accurately represent the data within two standard deviations, which is significantly broader.
C) 95%
This option is correct because it aligns with the empirical rule, stating that approximately 95% of the observations in a normal distribution lie within two standard deviations from the mean, capturing a substantial portion of the data.
D) 99.70%
This option is incorrect as it pertains to the data within three standard deviations of the mean. While it signifies a larger range, it does not answer the question regarding two standard deviations.
Conclusion
The correct answer is C) 95%, as it accurately reflects the empirical rule regarding the distribution of data in a normal distribution. Options A and B fail to capture the breadth of data within two standard deviations, while D overreaches by referencing three standard deviations. Thus, C is definitively the only accurate choice.