Question

According to the empirical rule, for a distribution that is symmetrical and bell-shaped (in particular, for a normal distribution) approximately how much of the data values will lie within two standard deviations on each side of the mean?

Answer 1

A sketch of the normal distribution is shown in the figure below.
The mean is μ, and the curve is symmetric about the mean.
The total area under the curve is 1.

The standard deviation is σ.
The interval (μ-σ, μ+σ) contains approximately 68% of the total area.
The interval (μ-2σ, μ+2σ) contains approximately 95% of the total area.

Answer: 95%