55. A data set is normally distributed with a mean of 30 and a standard deviation of 3. Which percentage of the data falls between the range of 24 and 30?
Answer: A
48%
In a normally distributed data set, the percentage of data that falls within a specific range can be determined using the properties of the normal distribution. For the range between 24 and 30, which represents one standard deviation below the mean, 48% of the data falls within this interval.
A) 48
This option is correct because it represents the percentage of data that lies between one standard deviation below the mean (24) and the mean itself (30) in a normal distribution, which is 48%.
B) 34
This option is incorrect because 34% represents the percentage of data that lies between the mean (30) and one standard deviation above the mean (33). It does not account for the data between one standard deviation below the mean and the mean.
C) 25
This option is incorrect as it does not accurately reflect any standard percentage related to the normal distribution. The percentage of data between 24 and 30 is not 25%, as this range spans a greater portion of the distribution.
D) 68
This option is incorrect because 68% refers to the total percentage of data that falls within one standard deviation of the mean, which encompasses the range from 27 to 33, not just between 24 and 30.
Conclusion
The correct answer is 48%, as it accurately describes the percentage of data within the specified range of a normally distributed data set. All other options misrepresent the distribution characteristics, failing to align with the properties of standard deviations in a normal distribution.