Question

According to the empirical rule, if the data form a "bell-shaped" normal distribution, ________ percent of the observations will be contained within 2 standard deviations around the arithmetic mean.

Answer 1

According to empirical rule, the area under the normal distribution or "bell-shaped curve", when plotted as a function of the z-parameter can be defined in terms of percentages.
The z-parameter (or z-score) is defined as

`z= (x- \mu )/( \sigma )`
where
x = value of random variable,
μ = the mean,
σ = standard deviation,

The total area under the curve = 1.
The curve below shows that within 2 standard deviations from the mean, the total area under the curve is 95% of the total area.



Answer: 95%