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Chapter 6: Q. 6.88 (page 276)

State the empirical rule as specialized to variables.

Short Answer

Expert verified

The percentage that is within one standard deviation of the mean is roughly 68.26%.

The percentage within two standard deviations of the mean is 95.44per cent.

Around 99.74per cent are within three standard deviations of the mean.

Step by step solution

01

Concept introduction

The quantity of one variable in algebraic equations is typically reliant on the position of another. If the data tuple isn't declared precisely, the variable's beginning value reflects the default value.

02

Explanation

Normal distributions have a bell shape to them. As a result, the empirical rule is as follows:

For the distributed variable with a bell shape,

- The percentage of observations that are within one standard deviation of the mean is roughly 68.26%.

- The percentage of observations that are within two standard deviations of the mean is 95.44%.

- Around of observations are within three standard deviations of the mean.

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