Assume we draw a simple random sample from a population having a mean of 100 and a standard deviation of 16. What is the probability that a sample mean will be within plus-or-minus two of the population mean for each of the following sample sizes?

Question

(a.) n = 50 ____________
(b.) n = 100
(c.) n = 200 ____________
(d.) n = 400 ____________

Answer 1

μ ± 2SE will always include approximately 95% of the possible means. However, the range of the possible means for the 95% will be smaller as the n increases.

SE (Standard Error of the mean) = SD/sq.root of n

(For smaller samples, you might want to use n-1.)

I hope this helps.