Construct the sampling distribution of the sample proportion of heads, for flipping a balanced coin

(a) Once.

(b) Twice. (Hint: The possible samples are (H, H), (H, T),

(T, H), (T, T).)

(c) Three times. (Hint: There are 8 possible samples.)

(d) Four times. (Hint: There are 16 possible samples.)

(e) Describe how the shape of the sampling distribution seems to be changing as the number of flips increases.