Chapter 5, Problem 5.62SE

Tossing a Coin A balanced coin is tossed three times. Let x equal the number of heads observed.

a. Use the formula for the binomial probability distribution to calculate the probabilities associated with $x=0,1,2,\text{and }3.$

b. Construct the probability distribution.

c. Find the mean and standard deviation of x, using these formulas:

   $\begin{array}{l}\mu =np\\ \sigma =\sqrt{npq}\end{array}$

d. Using the probability distribution in part b, find the fraction of the population measurements lying within one standard deviation of the mean. Repeat for two standard deviations. How do your results agree with Tchebysheff’s Theorem and the Empiric al Rule?