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A machine fills bags of rice. The masses of single bags have a standard deviation of 15 g…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A machine fills bags of rice. The masses of single bags have a standard deviation of g. An inspector weighs a random sample of bags and works out their mean mass. Find the standard error of the sample mean. Find it again for a sample of bags.
Need a reminder? The key ideaShow
The sampling distribution of is centred at . Its standard error is
For larger samples it is close to a normal curve, so about of sample means lie within standard errors of .
The worked solution
Have you tried it?
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. g.
Step 2. g.
Answer: g and g.
Check. Four times as many bags give half the standard error, as the square root rule says.
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