How do you determine the probability of a sample mean being a certain value?
To make this more concrete, suppose we have a population of 1000 values. the population mean is 50 and the standard deviation is 5.
How do we determine the probability of 20 random individuals from that population having a sample mean of 40, and a standard deviation of 6. What about the probability of them all being less than 40?
No, it's not homework. But I imagine this is a sort of common thing to solve, so if anyone could just point me in the direction of an online resource that talks about the relevant topic, that would be great.