suppose that x is a binomial random variable with n 5 p 78 and q 22 b for each value of x calcul

First, we need to calculate the probabilities for each value of x using the binomial probability

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Suppose that x is a binomial random variable with n = 5, p = 0.78, and q = 0.22. (b) For each value of x, calculate p(x). (Round final answers to 4 decimal places.) p(0) = ? p(1) = ? p(2) = ? p(3) = ? p(4) = ? p(5) = ? (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 μx, the variance σ^2x, and the standard deviation σx of this binomial distribution. Show that the formulas for μx, σ^2x, and σx given in this section give the same results. (Do not round intermediate calculations. Round final answers to μx in to 2 decimal places, σ^2x and σx in to 4 decimal places.) (i) 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 the next whole number and round down the upper interval to the previous whole number. (Round your answers to 4 decimal places. A negative sign should be used instead of parentheses.)

          Suppose that x is a binomial random variable with n = 5, p = 0.78, and q = 0.22.
(b) For each value of x, calculate p(x). (Round final answers to 4 decimal places.)
p(0) = ?
p(1) = ?
p(2) = ?
p(3) = ?
p(4) = ?
p(5) = ?
(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 μx, the variance σ^2x, and the standard deviation σx of this binomial distribution. Show that the formulas for μx, σ^2x, and σx given in this section give the same results. (Do not round intermediate calculations. Round final answers to μx in to 2 decimal places, σ^2x and σx in to 4 decimal places.)
(i) 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 the next whole number and round down the upper interval to the previous whole number. (Round your answers to 4 decimal places. A negative sign should be used instead of parentheses.)

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