Question

Suppose that x is a binomial random variable with n = 5, p = .66, and q = .34.

(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.)

P(x < 3) = P(x <= 2)

(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 μ_x, the variance, σ2x , and the standard deviation, σ_x, of this binomial distribution. Show that the formulas for μ_x , σ2x, and σ_x given in this section give the same results. (Do not round intermediate calculations. Round final answers to µ_x in to 2 decimal places, σ ²_x and σ_x in to 4 decimal places.)

μ_{x    ?}

σ_{x^2 ?}

σ_{x      ?}

(i) Calculate the interval [μ_x ± 2σ_x]. 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 4 decimal places. A negative sign should be used instead of parentheses.)

The interval is [ ___ , ____ ]

P( ____ <= x <= ____) = _____

Answer 1