You will decide that you will record then number of heads every time a coin is flipped 10 times in a variable X. After flipping the coin 30 times in total you calculate the sample mean for your X variable is 6 heads.

a) Is the sampling distribution approximately normal? explain using Central Limit Theorem

b) Now assume you flip the coin 300 times in total and calculate the sample mean for your X variable is 5.5 heads. Solve the standard deviation for the Population Distribution and the Sampling Distribution .

c) Based on part b) what is the probability of observing a sample mean as extreme (rare) as you did?

d) If you flipped your coin 3000 times total what would you expect to happen to your sample distribution? Justify.