Periodically, a sample of 20 items are randomly selected from a population that is normally distributed, the average is computed, and plotted. Which of the following statements is correct?
I. The average of the logarithms of the values is lognormally distributed.
II. The standard deviation of the averages is equal to the standard deviation of the individuals divided by the square root of 20.
III. The variance of the averages is equal to the variance of the individuals divided by the square root of 20.