Number of experiments to achieve mean value

[pavelcherepan]

Hi all! This is not a homework question, just a silly thing I've been working on.

I have a set of 11 random variables and one constant (that I don't know the value of). Every time I run an experiment all 11 variables assume a value of either 0 or 1 (all together). The question is simple: how to calculate the total number of experiments that I need to do in order for the average value of those 11 variables (from all experiments) to approach the mean of 0.5 to an accuracy of, let's say, 99.9%. After that I should be able to find out the value of my constant.

Thanks for the help!

Edited February 10, 2019 by pavelcherepan

[Bignose]

If all 11 variables and all experiments are independent and identically distributed, then you can use the binomial distribution to calculate what you need https://en.wikipedia.org/wiki/Binomial_distribution