Question

A data set has mean μ and standard deviation σ

. Which statement is correct?

A value chosen randomly from the data set will typically be contained in the interval [−μσ,μσ]
A value chosen randomly from the data set will typically be contained in the interval [μ−σ,μ+σ]
A value chosen randomly from the data set will typically be contained in the interval [μ,μ+σ]

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct statement is: A value chosen randomly from the data set will typically be contained in the interval [μ−σ,μ+σ]. This is because the standard deviation represents the average distance of data points from the mean, so typically about 68% of the data points will fall within 1 standard deviation of the mean in a normal distribution.