Suppose that x is a binomial random variable with n = 5, p = .20, and q = .80.
(b) For each value of x, calculate p(x). (Round final answers to 4 decimal places.)
(c) Find P(x = 3). (Round final answer to 4 decimal places.)
(d) Find P(x <= 3). (Do not round intermediate calculations. Round final answer to 4 decimal places.)
(e) Find P(x < 3). (Do not round intermediate calculations. Round final answer to 4 decimal places.)
(f) Find P(x >= 4). (Do not round intermediate calculations. Round final answer to 4 decimal places.)
(g) Find P(x > 2). (Do not round intermediate calculations. Round final answer to 4 decimal places.)
(h) Use the probabilities you computed in part b to calculate the mean mu x, the variance, sigma 2x
sigma
x
2
, and the standard deviation, sigma x, of this binomial distribution. Show that the formulas for mu x , sigma 2x
sigma
x
2
, and sigma x given in this section give the same results. (Do not round intermediate calculations. Round final answers to µx in to 2 decimal places, sigma 2x and sigma x in to 4 decimal places.)
(i) Calculate the interval [mu x pm 2sigma x]. Use the probabilities of part b to find the probability that x will be in this interval. (Round your answers to 4 decimal places. A negative sign should be used instead of parentheses.)