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## Theory on Estimating the Population Mean

Estimating the Mean:We are estimating the population mean, mu, not the sample mean, x bar.

:Population Standard Deviation KnownWhenever population standard deviation or sigma is identified, then mean has the normal (Z) distribution.

The maximum error of estimation is given by the formula for E is as shown below. The Z here is the z-score obtained from the normal table, or the bottom of t-table as described above. The z-score is a factor of level of confidence; therefore you might get in the habit of writing it later to the level of confidence.

E = Z_{α/2}(σ/√n)Once you have calculated E, now it is recommended to save the memory on your calculator. On TI-82, an excellent choice would be the letter E. The main reason for this is that the limits for the confidence interval are now found by adding and subtracting the maximum error of the estimate from or to the sample mean.

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