Independent random samples of n = 100 observations each are drawn from normal populations. The parameters of these populations are: Population 1: 1 =

Independent random samples of n = 100 observations each are drawn from normal populations. The parameters of these populations are:
– Population 1: µ1 = 300 and σ1 = 60;
– Population 2: µ2 = 290 and σ2 = 80.
Questions.
(a) Find the probability that the mean of Population 1 is between 294 and 306.
(b) Find the probability that the mean of Population 1 is greater than the mean of Population 2 by more than 20.