36. 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?
Answer: C
Approximately 68% of the data falls between 275 and 281.
In a normally distributed data set, about 68% of the values lie within one standard deviation from the mean. Given the mean of 278 and a standard deviation of 3, the range from 275 (278 - 3) to 281 (278 + 3) captures approximately 68% of the data.
A) 99
This option is incorrect because 99% refers to the data that falls within three standard deviations from the mean in a normal distribution. The specified range of 275 to 281 only covers one standard deviation, which is significantly less than 99%.
B) 32
This option is also incorrect as it does not align with the empirical rule for normal distributions. The value of 32% does not represent any common segment of the distribution; rather, it underestimates the percentage of data within one standard deviation from the mean.
C) 68
This option is correct because it accurately reflects the empirical rule, which states that approximately 68% of the data points in a normal distribution fall within one standard deviation of the mean. The calculations confirm that the range of 275 to 281 encompasses this portion of the distribution.
D) 95
This option is incorrect since 95% of the data in a normal distribution falls within two standard deviations from the mean. The range provided (275 to 281) only includes one standard deviation, thus falling short of encompassing 95% of the data.
Conclusion
The correct answer, 68%, is definitively right because it aligns with the established empirical rule regarding normal distributions. All other options either overestimate or underestimate the percentage of data within the specified range, failing to accurately represent the characteristics of a normal distribution.