Q&A for How to Use the Empirical Rule

To determine the percentage of people who have lost 10 pounds or more, you would need specific data from a study or survey that tracks weight loss in a population. Without such data, it's impossible to provide an accurate percentage. The concept of a percentile in this context would refer to where an individual's weight loss falls in comparison to others in a dataset. For example, if you are in the 80th percentile for weight loss, it means you have lost more weight than 80% of the people in that group. Again, determining this requires specific data on weight loss across a population.

In a normal distribution with a mean of 60 and a standard deviation of 17 you would expect to find approximately 95% of the data between the values of 26.68 and 93.32. ​

The empirical rule (or the 68-95-99.7 rule) is not used for finding the mean. It's used when the mean and standard deviation of a normally distributed dataset are known. It states that about 68% of values are within one standard deviation of the mean, 95% within two, and 99.7% within three. To find the mean, you typically sum all the values in a dataset and divide by the number of values.

Using the empirical rule, approximately 95% of values in a normally distributed data set lie within two standard deviations of the mean. With a mean of 3.05 kg and a standard deviation of 0.39 kg, a weight of 4 kg (about 2.44 standard deviations above the mean) would still fall within the normal range.

To find the weight of the chocolate bar that is 0.5 standard deviations above the mean, use the formula: X = 0.5 * σ + μ. Given a mean (μ) of 100 grams and a standard deviation (σ) of 10 grams, the calculation is: X = 0.5 * 10 + 100 = 105. Therefore, the chocolate bar weighs 105 grams.

To determine if the Empirical Rule is appropriate, assess the histogram's shape. If it is approximately bell-shaped with no significant skewness or outliers, then the Empirical Rule can be used to approximate data proportions.