54 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 x, the sample mean of the 40 observations.

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

Does your answer depend on the sample size?