Answer
If we take all possible samples of the same large size from a population and calculate the mean for each of these samples, then about 86.64% of the sample means will be within 1.5 standard deviations $( σ_\bar{x}\ $ ) of the population mean. Alternatively, we can state that if we take one sample ( of n $\geq$ 30) from a population and calculate the mean for this sample, the probability that this sample mean will be within 1.5 standard deviations $(σ_\bar{x}\ $) of the population mean is .8664.
P ( $\mu - 1.5σ_\bar{x}\ $\leq\ $\bar{x}\ $ $\leq \mu\ +1.5σ_\bar{x}\ $ =..9332-.0668 = .8664
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