The scores on a nationally administered standardized test are normally distributed. Which portion of the data is within two standard deviations of the mean?

Rationale

95% of the data is within two standard deviations of the mean in a normally distributed dataset.

In a normal distribution, approximately 95% of the data falls within two standard deviations from the mean, according to the empirical rule. This statistical principle illustrates how data is spread out around the mean, with most values clustering near the center.

A (50%) YOUR ANSWER

This choice refers to the proportion of data that lies within one standard deviation of the mean in a normal distribution. While a significant amount of data does fall within one standard deviation, it does not encompass the broader range covered by two standard deviations, which is necessary to achieve the 95% figure.

B (68%) YOUR ANSWER

This option is associated with the percentage of data that falls within one standard deviation of the mean in a normal distribution, not two. While 68% indicates a substantial portion, it is still below the 95% threshold relevant to the question, which specifically asks about the range encompassing two standard deviations.

C (95%) CORRECT

This is the correct answer, as it accurately reflects the empirical rule stating that approximately 95% of scores in a normally distributed dataset lie within two standard deviations of the mean. This characteristic is crucial for understanding the distribution of test scores and other normally distributed data.

D (99.70%) YOUR ANSWER

This choice pertains to the data that falls within three standard deviations of the mean in a normal distribution. While it represents an even broader range of data, it exceeds the scope of the question regarding two standard deviations, making it an incorrect option for this particular query.

Conclusion

In a normally distributed set of scores, 95% of the data lies within two standard deviations of the mean, as dictated by the empirical rule. This statistical property is fundamental for interpreting test scores and understanding the spread of data, while the other choices reflect incorrect percentages related to one or three standard deviations. Understanding this distribution is essential for effective data analysis and interpretation in standardized testing contexts.

The scores on a nationally administered standardized test are normally distributed. Which portion of the data is within two standard deviations of the mean?

95% of the data is within two standard deviations of the mean in a normally distributed dataset.

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