Each time an unbiased coin is flipped three times, the probability of getting 0, 1, 2, and 3 heads is 1/8, 3/8, 3/8, and 1/8, respectively. Therefore, with eight groups of three flips each, on the average, one group will yield 0 heads, three groups will yield 1 head, three groups will yield 2 heads, and one group will yield 3 heads.
(a) Obtaining uniform random numbers as instructed at the beginning of the Problems section, simulate the flips specified in part (a) and record the information indicated in part (a).
(b) Formulate a spreadsheet model for performing a simulation of three flips of the coin and recording the number of heads. Perform one replication of this simulation.
(c) Use this spreadsheet to generate a data table with 8 replications of the simulation. Compare this frequency distribution of the number of heads with the probability distribution of the number of heads with three flips.
(d) Repeat part (c) with 800 replications.