For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ − 2σ, μ + 2σ] is the closest to ______.Multiple Choice95%99.73%68%68.26%
Question
For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ − 2σ, μ + 2σ] is the closest to ______.Multiple Choice95%99.73%68%68.26%
Solution
The correct answer is 95%. This is a property of normally distributed random variables, often referred to as the Empirical Rule or the 68-95-99.7 rule. This rule states that for a normal distribution, almost all data will fall within three standard deviations of the mean. Specifically, about 68% of data will fall within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations. Therefore, the percent of observations that fall between [μ − 2σ, μ + 2σ] is closest to 95%.
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