7.64 Coin-tossing distributions For a single toss of a balanced coin, let x = 1 for a head and x = 0 for a tail.

a. Construct the probability distribution for x and calculate its mean. (You can think of this as the population distribution corresponding to a very long sequence of tosses.)

b. The coin is flipped 10 times, yielding 6 heads and 4 tails. Construct the data distribution.

c. Each student in the class should flip a coin 10 times and find the proportion of heads. Collect the sample proportion of heads from each student. Summarize the simulated sampling distribution by constructing a plot of all the proportions obtained by the students.

Describe the shape and variability of the sampling distribution compared to the distributions in parts a and b.

d. If you performed the experiment in part c a huge number of times, what would you expect to get for the (i) mean and (ii) standard deviation of the sample proportions?