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 ≥ 3).

g. Find. p(x > 3).

h. Use the probabilities you computed in part b to calculate the mean, , the variance, , and the standard deviation, , 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 [μ ( 2σx]. Use the probabilities of part b to find the probability that x will be in this interval.