Answer :
Final answer:
The student is asking how to use the Empirical (or 68-95-99.7) Rule to check if a set of data is normal. This rule applies to bell-shaped and symmetric distributions and states that about 68%, 95%, and 99.7% of the data falls within one, two, and three standard deviations of the mean, respectively.
Explanation:
The student is asking about how to check if a given dataset is normal using what is known as the Empirical Rule, also referred to as the 68-95-99.7 rule. This rule is used for distributions that are bell-shaped and symmetric.
The Empirical Rule states that for a bell-shaped distribution:
- About 68% of the data falls within one standard deviation of the mean.
- About 95% is within two standard deviations.
- And roughly 99.7% is within three standard deviations.
It's imperative to note that this rule only applies if the distribution of the data is bell-shaped and symmetric. For example, if you have a dataset with a mean score of 65 and you assume that the distribution of your data is normal, you can expect approximately 95% of the data to be within two standard deviations of this mean.
If you're conducting a hypothesis test at a 5% significance level with this data, the data outside of the range defined by two standard deviations from the mean would be considered statistically significant.
Learn more about Empirical rule here:
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