A balanced coin is tossed three times. Let Y equal the number of heads observed. a. Use the formula for the binomial probability distribution to calculate the probabilities associated with Y = 0, 1, 2, and 3.
b. Construct a probability distribution.
c. Find the expected value and standard deviation of Y, using the formulas E(Y ) = np and V (Y ) = npq.
d. Using the probability distribution from part (b), find the fraction of the population measurements lying within 1 standard deviation of the mean.