Question

The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell shaped distribution) that fall within two standard deviations of their mean is approximately:...................

Answer 1

The Empirical Rule indicates that for a bell-shaped distribution, roughly 95 percent of data falls within two standard deviations of the mean.

Step-by-step explanation:

The Empirical Rule states that the approximate percentage of measurements in a data set that fall within two standard deviations of their mean, assuming the data set has a bell-shaped distribution, is approximately 95 percent.

For a normal distribution, which is symmetric, it's observed that:

• About 68 percent of the data falls within one standard deviation of the mean.
• About 95 percent of the data falls within two standard deviations of the mean.
• More than 99 percent of the data falls within three standard deviations of the mean.

This pattern is well-established in statistics and is crucial when analyzing data and predicting outcomes based on the normal probability distribution.