Let be random samples from a normal distribution where the mean is 2 and the variance is 4. How large must n be in order that ?
We are computing for the sample mean of our random sample that was given in the problem. By definition, . So rewrite the equation so we can transform the data to make the mean 0 and the standard deviation 1. If I do that, I get,
This means that
This also means that
I am not really sure what to do after this step. I am trying to use the definition of the normal distribution, however that was too difficult to do.
Do you guys know what to do after this step?