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 mean.

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

c.) For a 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.