61 The binomial probability distribution is a family of probability distributions with each single distribution depending on the values of n and p . Assume that x is a binomial random variable with n = 4.

a. Determine a value of p such that the probability distribution of x is symmetric.

b. Determine a value of p such that the probability distribution of x is skewed to the right.

c. Determine a value of p such that the probability distribution of x is skewed to the left.

d. Graph each of the binomial distributions you obtained in parts a , b , and c . Locate the mean for each distribution on its graph.

e. In general, for what values of p will a binomial distribution be symmetric? skewed to the right? skewed to the left?