The Problem

The average hourly wage of fast-food workers employed by a nationwide chain is $5.55. The standard deviation is $1.15. If a sample of 50 workers is selected, find the probability that the mean of the sample will be between $5.25 and $5.90.

Since this problem deals with a distribution of averages, the Cental Limit Theorem applies. Thus, the distribution is normal with standard deviation of . The TI84 has a function that preforms the required calculation. That function is

From the statement of the problem, we have = 5.55, = 1.15, n = 50, = 5.25, and = 5.90.

From the home screen, press 2nd Vars[DISTR] and then press 2 to select 2:normalcdf(. Press ENTER. Type 5.25 ENTER 5.90 ENTER 5.55 ENTER square root of 50 then press ENTER twice.

The results are shown below.

Thus, the probability that the mean of the sample will be between $5.25 and $5.90 is about 95%.


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