# Question

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?

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?

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