A random sample of size n = 50 is taken from a large population with mean 15 and variance 4, but unknown distribution.
(i) What is the standard deviation σX¯ of the sample mean?
(ii) If the sample size were reduced by 50%, what will be the new standard deviation σX¯ of the sample mean?
(iii) To reduce the standard deviation to 50% of the value in (i), what sample size will be needed?