Z of 95.44% / 2 = Z of 47.72% = 1.9991

-1.9991 <= our Z <= 1.9991 ( you can find z value here: http://davidmlane.com/hyperstat/z_table.html ) mean = 26$; the value can swing to the left(25$) or the right(27$) but shouldn't be more extreme than those two 95.44% at a time. so, we choose 27$ as xbar and our Z = 1.9991 = (xbar - u) / (S.D. / n^0.5) n^0.5 = 1.9991*S.D / (xbar-u) = 1.9991*5.65 / (27 - 26) n^0.5 = 11.295 ; n = 127.58 or 128 so you need 128 samples. ============ 2. Central Again? ========== Assumption: pop. mean = u = 42 pop S.D. = 11 Average number = number of people in all 5 days and average it So, we have 5 random variables ( 1 per day ), therefore, n = 5 Z = (xbar - u) / ( S.D. / n^0.5 ) Z = (50 - 42) / ( 11 / 5^0.5 ) = 1.626 "exceed 50" mean that we need find the area to the right of z. Answer: P(xbar >= 50) = P(Z >= 1.626) = 5.2%