Question

Let X be normally distributed with mean μ = 18 and standard deviation σ = 8. [You may find it useful to reference the z table.]

a. Find P(X ≤ 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

b. Find P(X > 4). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

c. Find P(8 ≤ X ≤ 16). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

d. Find P(12 ≤ X ≤ 22). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

a)

                          

                           = P(Z < -2)

                           = 0.0228

b)

                          

                           = P(Z > -1.75)

                           = 1 - P(Z < -1.75)

                           = 1 - 0.0401

                           = 0.9599

c)

                                     

                                      = P(-1.25 < Z < -0.25)

                                      = P(Z < -0.25) - P(Z < -1.25)

                                      = 0.4013 - 0.1056

                                      = 0.2957

d)

                                     

                                      = P(-0.75 < Z < 0.5)

                                      = P(Z < 0.5) - P(Z < -0.75)

                                      = 0.6915 - 0.2266

                                      = 0.4649