Question

Suppose x has a distribution with μ = 22 and σ = 16.

(a) If a random sample of size n = 33 is drawn, find μ_x, σ_x and P(22 ≤ x ≤ 24). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(22 ≤ x ≤ 24) =

(b) If a random sample of size n = 59 is drawn, find μ_x, σ_x and P(22 ≤ x ≤ 24). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(22 ≤ x ≤ 24) =

Answer 1

µ = 22

σ = 16

a) n = 33

µ_x = µ = 22

σ_x = σ / sqrt(n) = 16 / sqrt(33) = 2.79

                                    

                                     = P(0 < Z < 0.72)

                                     = P(Z < 0.72) - P(Z < 0)

                                     = 0.7642 - 0.5

                                     = 0.2642

b) n = 59

µ_x = µ = 22

σ_x = σ / sqrt(n) = 16 / sqrt(59) = 2.08

                                    

                                     = P(0 < Z < 0.96)

                                     = P(Z < 0.96) - P(Z < 0)

                                     = 0.8315 - 0.5

                                     = 0.3315