Assume Xi is distributed normal, with mean 25, standard deviation 2. Assume a random sample of 25 independent X i ‘s was taken.
(a) Find the expected value and the standard deviation of the sample average.
(b) Find the expected value and the standard deviation of the total.
(c) Explain intuitively why the standard deviation from (a) is smaller than the standard deviation of Xi.
(d) Explain intuitively why the standard deviation from (b) is larger than the standard deviation of Xi.
