Refer to Exercise 5.62. Suppose the coin is definitely unbalanced and the probability of a head is equal to p = .1. Follow the instructions in parts a, b, c, and d. Note that the probability distribution loses its symmetry and becomes skewed when p is not equal to 1/2.
Exercise 5.62
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, and 3.
b. Construct the probability distribution.
c. Find the mean and standard deviation of x, using these formulas:
µ = np
σ = √npq
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 Empirical Rule?