A data set has mean μ and standard deviation σ . Which statement is correct?(1 point) Responses A value chosen randomly from the data set will typically be contained in the interval [μ−σ,μ] . A value chosen randomly from the data set will typically be contained in the interval left bracket mu minus sigma comma mu right bracket. 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 left bracket mu minus sigma comma mu plus sigma right bracket. 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 left bracket negative mu over sigma comma mu over sigma right bracket. A value chosen randomly from the data set will typically be contained in the interval [μ,μ+σ] .
1 answer
The correct statement is:
A value chosen randomly from the data set will typically be contained in the interval [μ−σ, μ+σ].
This reflects the empirical rule (or the 68-95-99.7 rule), which states that in a normal distribution, approximately 68% of the data points fall within one standard deviation (σ) of the mean (μ). Specifically, this means that most values will lie in the interval [μ - σ, μ + σ].
