Question

Let z denote a standard normal random variable.

a. Find P(z > 1.48).

b. Find P(-0.44 < z < 2.68).

c. Determine the value of which

satisfies P(z > z. ) = 0.7995. d. Find P(z < –0.87).

Answer 1

Part a)

P ( Z > 1.48 ) = 1 - P ( Z < 1.48 ) = 1 - 0.9306 = 0.0694

Part b)

P ( -0.44 < Z < 2.68 ) = P ( Z < 2.68 ) - P ( Z < -0.44 ) = 0.9963 - 0.33 = 0.6664

Part c)

P ( Z > ? ) = 0.7995

P ( Z > ? ) = 1 - P ( Z < ? ) = 1 - 0.7995 = 0.2005

Looking for probability 0.2005 in standard normal table to find the critical value

Z = - 0.84

P ( Z > -0.84 ) = 0.7995

Part d)

P( Z < –0.87 )

Z = -0.87 = P ( Z < -0.87 ) = 0.1922

Looking for critical value z = -0.87 in standard normal table to find the probability.