Suppose that x is a binomial random variable with n = 5, p = .3, and q = .7.
a. Write the binomial formula for this situation and list the possible values of x.
b. For each value of x, calculate p(x), and graph the binomial distribution.
c. Find P(x = 3).
d. Find P(x < 3).
e. Find P(x < 3).
f. Find P(x > 4).
g. Find P(x > 2).
h. Use the probabilities you computed in part b to calculate the mean, μx, the variance, σ2x, and the standard deviation, σx of this binomial distribution. Show that the formulas for μx, σ2x, and σx given in this section give the same results.
i. Calculate the interval [μx ± 2σx]. Use the probabilities of part b to find the probability that x will be in this interval.