This is my assignment for Statistics, I answered the question but I want to make sure is well answered and If I am answering right both “explain the empirical rule” and the “when can it be used?”. Please feel free to do any changes. Thank you very much.
-Explain the empirical rule. When can it be used?
The Empirical Rule also referred to as the Three Sigma Rule, or the 68-95-99.7 Rule, can be used to solve many problems that involve a normal distribution, where almost all datafalls within three standard deviations of the mean. For data sets having a normal, bell-shaped distribution, the following properties apply: the empirical rule shows that 68% will fall within the first standard deviation(which means 68% of the data will be located within one standard deviation symmetric to the mean), 95% within the first two standard deviations (95% of the data will be located within two standard deviations symmetric to the mean), and 99.7% will fall within the first three standard deviations of the mean (meaning 99.7% of the data will be located within three standard deviations symmetric to the mean).
Moreover, the Empirical Rule is most often used for forecasting final outcomes. Before exact data is collected, and after a standard deviation is calculated; this rule is used as a rough estimate to the outcome of the impending data. This probabilitycan be used in the meantime as gathering appropriate data may be time consuming, or even impossible to obtain.
For example, suppose the data meets the conditions for which the empirical rule applies. If the mean of the distribution is 10, and the standard deviation of the distribution is 2, then about 68% of the data will be between the numbers 8 and 12 since 10-2 =8 and 10+2 = 12. We would expect approximately 95% of the data to be located between the numbers 6 and 14 since 10-2(2) = 6 and 10 + 2(2) = 14. Finally, almost all of the data will be between the numbers 4 and 16 since 10 – 3(2) = 4 and 10 + 3(2) = 16.
Your understanding of the empirical rule looks thorough. Your reasoning is sound and the example calculations that are included add strength to your final point. Well done.
There is one other point that …
An edited response regarding the empirical rule and its proper usage in statistics. Includes additional material to include for a complete answer.