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A single measurement of a length has a random error with the spread 0.5 mm.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A single measurement of a length has a random error with the spread 0.5 mm. How many measurements must be averaged so that the standard error of the mean is not more than 0.05 mm? Check your answer with a simulation: make 5000 experiments of that many measurements, and find the spread of their means.
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.
Plan. The standard error is . Set it to 0.05 and solve for : , so .
Check. The simulated spread of the means is 0.0507, close to the 0.05 that we wanted. Notice what the answer says: to reduce the uncertainty from 0.5 to 0.05, a factor of 10, you need 100 times as many measurements.
Answer: 100 measurements.
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