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The times that patients wait at a made-up clinic have mean 50 minutes and standard deviation 12…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The times that patients wait at a made-up clinic have mean minutes and standard deviation minutes. The times are skewed, with a few very long waits. A manager takes a random sample of patients each week and works out their mean wait. Explain why the sample mean is close to a normal curve. Find its standard error. Find the probability that a week's sample mean is more than minutes. Find the probability that it lies between and minutes. Give the probabilities to four decimal places.
Need a reminder? The key ideaShow
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Shape. The sample of is large, so by the central limit theorem is close to normal, even though single waits are skewed.
Step 2. Spread. min.
Step 3. Above minutes. . The area above is about .
Step 4. Between. From to the area is about .
Answer: minutes, and .
Watch out. Using minutes in place of the standard error gives , and a probability near . That would describe one patient, not the mean of .
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