A normally distributed data set of lab values has a mean of 278 and a standard deviation of 3. Which percentage of the data falls between 275 and 281?

Rationale

Approximately 68% of the data falls between 275 and 281 in a normally distributed data set.

In a normal distribution, about 68% of the data lies within one standard deviation of the mean. Given a mean of 278 and a standard deviation of 3, the range from 275 to 281 encompasses this interval, thus capturing the majority of the data.

A (99) YOUR ANSWER

This choice refers to the empirical rule, which states that approximately 99.7% of data falls within three standard deviations of the mean. While this percentage indicates a much broader range than the interval specified, it does not accurately reflect the percentage of data within just one standard deviation, which is the focus of the question.

B (32) YOUR ANSWER

This percentage does not correspond to any standard interval in a normal distribution. The empirical rule does not support a 32% figure for data falling between any specific points, making this choice irrelevant in the context of the given mean and standard deviation.

C (68) CORRECT

As explained, this option accurately reflects the empirical rule, which indicates that approximately 68% of data lies within one standard deviation from the mean in a normal distribution. Since the range from 275 (278 - 3) to 281 (278 + 3) covers one standard deviation, this choice is correct.

D (95) YOUR ANSWER

This choice represents the percentage of data that falls within two standard deviations of the mean. Although it is a significant figure in the context of a normal distribution, it does not apply to the interval between 275 and 281, which is confined to one standard deviation.

Conclusion

In summary, the percentage of data falling between 275 and 281 in a normally distributed data set with a mean of 278 and a standard deviation of 3 is approximately 68%. This value aligns with the empirical rule, highlighting how the distribution of data is concentrated within one standard deviation around the mean. Other choices reflect either broader or unrelated ranges that do not apply to the question asked.

A normally distributed data set of lab values has a mean of 278 and a standard deviation of 3. Which percentage of the data falls between 275 and 281?

Approximately 68% of the data falls between 275 and 281 in a normally distributed data set.

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