Answer :
Final answer:
To have 99.7% of all sample means within 1 point of the population mean, the required standard deviation of the sample mean (bar(x)) must be 1/3.
Explanation:
The question is asking for the standard deviation that a sample mean (denoted as bar(x)) must have so that 99.7% of all sample means will be within 1 point of the population mean (mu). This scenario is described by the Empirical Rule, specifically the part about 99.7% of the data (or sample means, in this context) being within three standard deviations of the mean.
Since we want bar(x) to be within 1 point of mu, and we know that we're dealing with three standard deviations to cover 99.7% of samples according to the Empirical Rule, we can set up the following equation:
3 * (Standard Deviation of bar(x)) = 1
Solving for the standard deviation (sigma), we get:
Standard Deviation of bar(x) = 1/3
