Answer :
Final answer:
The rule of 68-95-99.7 indicates that approximately 99.7% of the data will fall within three standard deviations of the mean in a normal distribution.
Explanation:
The rule of 68-95-99.7, also known as the Empirical Rule, states that in a normal distribution, approximately 99.7% of the data will fall within three standard deviations of the mean. This rule is applicable to data with a bell-shaped and symmetric distribution, where the mean, median, and mode are all the same. It's important to remember that the percentages 68%, 95%, and 99.7% correspond to distances of one, two, and three standard deviations from the mean, respectively.
To understand the Empirical Rule more completely, it's useful to know that approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and 99.7% within three standard deviations. The z-scores for these standard deviations are -1 and 1, -2 and 2, and -3 and 3, respectively. This rule is especially important when studying the Normal or Gaussian probability distribution.
