A random sample of 40 observations is to be drawn from a large population of measurements. It is known that 30% of the measurements in the population are 1’s, 20% are 2’s, 20% are 3’s, and 30% are 4’s.
a. Give the mean and standard deviation of the (repeated) sampling distribution of , the sample mean of the 40 observations.
b. Describe the shape of the sampling distribution of . Does your answer depend on the sample size?