Question
Pick an answer The following dataset has a mean of 10.38 and a standard deviation of 0.80. Using the Empirical Rule, determine if a normal curve can be used to model the data. (1 point) 55 percent of the data falls within 1 standard deviation of the mean. A normal curve can not be used to model the data, because this is not approximately 68% of the data. 52 percent of the data falls within 1 standard deviation of the mean. A normal curve can be used to model the data, because this is approximately 50% of the data. 73 percent of the data falls within 1 standard deviation of the mean. A normal curve can be used to model the data, because this is approximately 68% of the data. 30 percent of the data falls within 1 standard deviation of the mean. A normal curve can not be used to model the data, because this is not approximately 50% of the data.
Answers
GPT-4o mini
To determine if a normal curve can be used to model the data using the Empirical Rule, we need to know that according to the Empirical Rule:
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.
Now, evaluating the options:
1. **55 percent of the data falls within 1 standard deviation of the mean.** This is not approximately 68%, so a normal curve cannot be used to model the data.
2. **52 percent of the data falls within 1 standard deviation of the mean.** This is not approximately 68%, so a normal curve cannot be used to model the data.
3. **73 percent of the data falls within 1 standard deviation of the mean.** This is somewhat close but still not in the range of 68%, thus a normal curve cannot be modelled with this data.
4. **30 percent of the data falls within 1 standard deviation of the mean.** This is not even close to 68% and further confirms that a normal curve cannot be used to model the data.
Based on the options, none of them fits the criteria for the Empirical Rule about a normal distribution. However, options 1, 2, and 4 explicitly state that a normal curve cannot be used, which is correct based on the values provided.
If we had to select the most accurate statement from the given options regarding non-normality:
**55 percent of the data falls within 1 standard deviation of the mean. A normal curve can not be used to model the data, because this is not approximately 68% of the data.**
This option correctly applies the Empirical Rule but note that there is room for interpretation given the wording; however, it correctly states that a normal distribution cannot be used.
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.
Now, evaluating the options:
1. **55 percent of the data falls within 1 standard deviation of the mean.** This is not approximately 68%, so a normal curve cannot be used to model the data.
2. **52 percent of the data falls within 1 standard deviation of the mean.** This is not approximately 68%, so a normal curve cannot be used to model the data.
3. **73 percent of the data falls within 1 standard deviation of the mean.** This is somewhat close but still not in the range of 68%, thus a normal curve cannot be modelled with this data.
4. **30 percent of the data falls within 1 standard deviation of the mean.** This is not even close to 68% and further confirms that a normal curve cannot be used to model the data.
Based on the options, none of them fits the criteria for the Empirical Rule about a normal distribution. However, options 1, 2, and 4 explicitly state that a normal curve cannot be used, which is correct based on the values provided.
If we had to select the most accurate statement from the given options regarding non-normality:
**55 percent of the data falls within 1 standard deviation of the mean. A normal curve can not be used to model the data, because this is not approximately 68% of the data.**
This option correctly applies the Empirical Rule but note that there is room for interpretation given the wording; however, it correctly states that a normal distribution cannot be used.