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"The mass of some kids of $10$ weeks old follows a normal distribution with standard deviation of $87$g. ¿How many data is sufficient to estimate, with a $95$% confidence, the average mass of that population with an error no higher than $15$g"

This problem is in my exercise guide and i don't know how to do this. I never faced a problem like this before and i need some hints.

PS: I thought that "¿How many data...? refers to the sample size, but i'm not sure. I apologize if it is not the right approach

Sorry about the english.

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Yes, "how many data?" refers to the sample size $n$.

The key is that the width of your $95\%$ confidence interval will be roughly proportional to $1/\sqrt{n}$ (in fact here, since the model is a normal with known variance, it is exactly proportional to that). If you look up "z statistic" or something like that you should be able to find that the half-width of the $95\%$ confidence interval (i.e. the error) is $1.96\cdot\frac{\sigma}{\sqrt{n}}$ where the $1.96$ number comes from the $97.5\%$ quantile of the normal distribution.

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  • $\begingroup$ (+1) Perhaps see also. $\endgroup$
    – BruceET
    Commented Jul 7, 2018 at 22:51

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