Question
Use the Empirical Rule to determine the statement that is false. (2 points)
Responses
The Empirical Rule is a guideline as to how data is spread out in a normal distribution.
The Empirical Rule is a guideline as to how data is spread out in a normal distribution.
The percentage of data that is within one standard deviation of the mean is approximately 34%.
The percentage of data that is within one standard deviation of the mean is approximately 34%.
The percentage of data that is within two standard deviations of the mean is approximately 95%.
The percentage of data that is within two standard deviations of the mean is approximately 95%.
The percentage of data that is within three standard deviations of the mean is approximately 99.7%.
Responses
The Empirical Rule is a guideline as to how data is spread out in a normal distribution.
The Empirical Rule is a guideline as to how data is spread out in a normal distribution.
The percentage of data that is within one standard deviation of the mean is approximately 34%.
The percentage of data that is within one standard deviation of the mean is approximately 34%.
The percentage of data that is within two standard deviations of the mean is approximately 95%.
The percentage of data that is within two standard deviations of the mean is approximately 95%.
The percentage of data that is within three standard deviations of the mean is approximately 99.7%.
Answers
GPT-4o mini
To determine which statement is false regarding the Empirical Rule, let's review the statements:
1. **The Empirical Rule is a guideline as to how data is spread out in a normal distribution.**
(This statement is true.)
2. **The percentage of data that is within one standard deviation of the mean is approximately 34%.**
(This statement is false. The correct percentage is approximately 68% within one standard deviation, not 34%.)
3. **The percentage of data that is within two standard deviations of the mean is approximately 95%.**
(This statement is true.)
4. **The percentage of data that is within three standard deviations of the mean is approximately 99.7%.**
(This statement is true.)
Thus, the false statement is the one regarding the percentage of data within one standard deviation of the mean, which is incorrectly stated as approximately 34%. It should be approximately 68%.
1. **The Empirical Rule is a guideline as to how data is spread out in a normal distribution.**
(This statement is true.)
2. **The percentage of data that is within one standard deviation of the mean is approximately 34%.**
(This statement is false. The correct percentage is approximately 68% within one standard deviation, not 34%.)
3. **The percentage of data that is within two standard deviations of the mean is approximately 95%.**
(This statement is true.)
4. **The percentage of data that is within three standard deviations of the mean is approximately 99.7%.**
(This statement is true.)
Thus, the false statement is the one regarding the percentage of data within one standard deviation of the mean, which is incorrectly stated as approximately 34%. It should be approximately 68%.