Suppose that x is a binomial random variable with n = 5, p = .60, and q = .40.

(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 _x, the variance, 2xx2 , and the standard deviation, _x, of this binomial distribution. Show that the formulas for _x , 2xx2 , and _x given in this section give the same results. (Do not round intermediate calculations. Round final answers to _x in to 2 decimal places, ²_x and _x in to 4 decimal places.)

(i) Calculate the interval [_x 2_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.)