Suppose you draw a sample of size 5 where each observation comes from a Bernoulli distribution with probability of success equal to 0.4.

When answering the questions below, make sure to explain your answers (show how you got the answers). More than half of the points for each question are allocated to your explanations. Keep 4 digits after the period for all questions (e.g., 2.4505).

a) Develop the sampling distribution for the sample mean in this case. Use a table and show your work. (4 points)

b) What is the standard error for this sampling distribution? Show your work. (3 points)