A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.

a) for a sample of size 10, state the mean of the sample.

b) for a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean").

c) for sample of size 35, state the mean of the sample mean.

d) for a sample of size 35, state the standard deviation of the sample mean (the "standard error of the mean").

e) true or false: as sample size increases, standard deviation of the sample mean (the "standard error of the mean") also increases.