Question

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.1) = (b) P(z < -0.1) = (c) P(0.40 < z < 0.84) = (d) P(-0.84 < z < -0.40) = (e) P(-0.40 < z < 0.84) = (f) P(z > -1.25) = (g) P(z < -1.51 or z > 2.50) =

Answer 1

Part a)

P ( Z < 0.1 ) = 0.5398

Part b)

P ( Z < -0.1 ) = 0.4602

Part c)

P ( 0.4 < Z < 0.84 ) = P ( Z < 0.84 ) - P ( Z < 0.4 )
P ( 0.4 < Z < 0.84 ) = 0.7995 - 0.6554
P ( 0.4 < Z < 0.84 ) = 0.1441

part d)

P ( -0.84 < Z < -0.4 ) = P ( Z < -0.4 ) - P ( Z < -0.84 )
P ( -0.84 < Z < -0.4 ) = 0.3446 - 0.2005
P ( -0.84 < Z < -0.4 ) = 0.1441

Part e)

P ( -0.4 < Z < 0.84 ) = P ( Z < 0.84 ) - P ( Z < -0.4 )
P ( -0.4 < Z < 0.84 ) = 0.7995 - 0.3446
P ( -0.4 < Z < 0.84 ) = 0.455

Part f)

P ( Z > -1.25 ) = 1 - P ( Z < -1.25 )
P ( Z > -1.25 ) = 1 - 0.1056
P ( Z > -1.25 ) = 0.8944

Part g)

P ( -1.51 < Z < 2.5 ) = P ( Z < 2.5 ) - P ( Z < -1.51 )
P ( -1.51 < Z < 2.5 ) = 0.9938 - 0.0655
P ( -1.51 < Z < 2.5 ) = 0.9283
Required probability = 1 - 0.9283 = 0.0717