Solve the following problem:
Q: Suppose that x is a binomial random variable with n = 5, p = 0.2, and q = 0.8.
(a) For each value of x, calculate p(x), and graph the binomial distribution. (Round final answers to 5 decimal places.)
p(0) = , p(1) = , p(2) = , p (3) = ,
p(4) = , p(5) =
(b) Find P(x = 3).
(c) Find P(x ≤ 3).
(d) Find P(x < 3).
(e) Find P(x ≥ 4).
(f) Find P(x > 2)
(g) Use the probabilities you computed in part b to calculate the mean, μx, the variance, σ 2x, 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. (Do not round intermediate calculations. Round final answers to µx and σ 2x in to 2 decimal places, and σx in to 6 decimal places.)
(h) Calculate the interval [μx ± 2σx]. Use the probabilities of part b to find the probability that x will be in this interval. Hint: When calculating probability, round up the lower interval to next whole number and round down the upper interval to previous whole number. (Round your answers to 5 decimal places. A negative sign should be used instead of parentheses.)The interval is [, ]