State which of the following statements are true or false. If false, briefly explain why.

a) The sampling distribution of the sample mean is denoted by X.

b) The sampling distribution of the sample mean is the population from which the sample is drawn.

c) The sampling distribution of the sample mean will be approximately normal if we take lots of samples.

d) The sampling distribution of the sample mean is the value obtained by summing the values in the sample and dividing by the number of observations in the sample. e) The sampling distribution of the sample mean shows us the distribution of possible values that the sample mean could take, generated by calculating the sample mean for repeated samples of the same size, from the original population.