Question
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
The Empirical Rule states that for a normal distribution:
- 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.
To determine whether a normal curve can be used to model the data based on the percentages you provided, we need to compare the given percentages to the values from the Empirical Rule.
1. If the percentage is around 68% for 1 standard deviation, then a normal curve can be used to model the data.
2. If the percentage deviates significantly from 68%, it suggests that the data may not follow a normal distribution.
Analyzing each option provided:
- **55 percent of the data falls within 1 standard deviation of the mean.** (Not approximately 68%)
- **52 percent of the data falls within 1 standard deviation of the mean.** (Not approximately 68% and closer to 50%)
- **73 percent of the data falls within 1 standard deviation of the mean.** (This is greater than 68%, which may indicate some deviations but could still suggest a normal distribution.)
- **30 percent of the data falls within 1 standard deviation of the mean.** (Not close to 68%, indicates non-normal distribution.)
Given these considerations, the correct conclusion is:
**A normal curve can not be used to model the data, because this is not approximately 68% of the data.**
Thus, if the values of 55% or 52% were given, a normal curve would definitely not be appropriate. If 73% were assessed, further investigation would be necessary, as while it is above 68%, it might still indicate a relatively normal distribution with a slight skew. Ultimately, if the key requirement of approximately 68% is not met, we reject the use of a normal distribution.
- 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.
To determine whether a normal curve can be used to model the data based on the percentages you provided, we need to compare the given percentages to the values from the Empirical Rule.
1. If the percentage is around 68% for 1 standard deviation, then a normal curve can be used to model the data.
2. If the percentage deviates significantly from 68%, it suggests that the data may not follow a normal distribution.
Analyzing each option provided:
- **55 percent of the data falls within 1 standard deviation of the mean.** (Not approximately 68%)
- **52 percent of the data falls within 1 standard deviation of the mean.** (Not approximately 68% and closer to 50%)
- **73 percent of the data falls within 1 standard deviation of the mean.** (This is greater than 68%, which may indicate some deviations but could still suggest a normal distribution.)
- **30 percent of the data falls within 1 standard deviation of the mean.** (Not close to 68%, indicates non-normal distribution.)
Given these considerations, the correct conclusion is:
**A normal curve can not be used to model the data, because this is not approximately 68% of the data.**
Thus, if the values of 55% or 52% were given, a normal curve would definitely not be appropriate. If 73% were assessed, further investigation would be necessary, as while it is above 68%, it might still indicate a relatively normal distribution with a slight skew. Ultimately, if the key requirement of approximately 68% is not met, we reject the use of a normal distribution.