If a population follows a normal distribution with mean 10 and standard deviation 2, show that

a) If X is the value of a randomly sampled observation from this population, it has an expected value of 10.

b) If a sample of 25 observations is taken, its sample mean also has an expected value of 10.

c) If X is the value of a randomly sampled observation from this population, it has a standard deviation of 2.

d) If a sample of 25 observations is taken, its sample mean has a standard deviation of 0.4.

e) If a sample of 36 observations is taken, its sample mean has a standard error of 0.33.