A random sample of 50 observations is to be drawn from a large population of measurements. It is known that 40%

of the measurements in the population are 1’s, 20% are 2’s, 30% are 3’s, and 10% are 4’s.

a. Give the mean and standard deviation of the (repeated)

sampling distribution of x, the sample mean of the 50 observations.

b. Describe the shape of the sampling distribution of x.

Does your answer depend on the sample size?