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, s2xsx2 , and the standard deviation, sx, of this binomial distribution. Show that the formulas for x , s2xsx2 , and sx given in this section give the same results. (Do not round intermediate calculations. Round final answers to x in to 2 decimal places, s 2x and sx in to 4 decimal places.)(i) Calculate the interval [x 2sx]. 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.)MathStatistics and Probability COMM 215
