Suppose Bert and Ernie are each using simulations to describe the sampling distribution from a population that is skewed left with a mean of 50 and a standard deviation of 10. Bert obtains 1000 random samples of size n=3 from the population, finds the mean of the 1000 samples, draws a histogram of the means, finds the mean of the means, and determines the standard deviation of the means. Ernie does the same simulation but obtains 1000 random samples of size n = 30 from the population.

Please provide at least one source based on your answer.

• Describe the shape you expect for Bert's distribution of sample means.Describe the shape you expect for Ernie's distribution of sample means.
• What do you expect the mean of Bert's distribution to be? What do you expect the mean of Ernie's distribution to be?
• What do you expect the standard deviation of Bert's distribution to be? What do you expect the standard deviation of Ernie's distribution to be?
• Explain why you expect Bert and Ernie's results to be the same or different.