#### 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 98.76% of the sample means will be within 2.5 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 2.5 standard deviations $(σ_\bar{x}\ $) of the population mean is .9876.
P ( $\mu - 2.5σ_\bar{x}\ $\leq $\bar{x}\ $ $\leq \mu\ +2.5σ_\bar{x}\ $ =.9938-.0062 =.9876

#### Work Step by Step

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