The Problem

A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room per day. The standard deviation of the population is 4. Find the 99% confidence interval of the mean number of ER patients treated each day.

From the statement of the problem we have n = 48, = 38, and = 4. We are looking for a 99% confidence interval of the mean, where n > 30 and the standard deviation is known. Thus, we use the following TI83/84 ZInterval function.

Press STAT and right arrow twice to TESTS. Press 7 to select 7:ZInterval. If Stats is not selected, arrow right and then press ENTER to select it. Arrow down once and type 4 after :. Arrow down once and enter 38 after :. Arrow down once more and type 48 after n:. Arrow down once and type .99 after C-level:.

Arrow down one last time and press ENTER. The calculation will now be preformed, and the results are shown below.

The 99% confidence interval of the mean is 36.513 < < 39.487.

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