Let z denote a random variable having a normal distribution

Let z denote a random variable having a normal distribution with = 0 and = 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 < -1.49 or z > 2.50) =

Solution

Z ~ N (0 , 1)

a.) P( Z < 0.1) = 0.5398

b.) P( z < -0.1) = 0.4632

c.) P( 0.4 < z < 0.84) = P( z < 0.84) - P (z < 0.40)

   = 0.7995 - 0.6554

   = 0.1441

d.) P( -0.84 < z< -0.40) = P (z < -0.40) - P( z< -0.84)

   = 0.3446 - 0.2005

   = 0.1441

e.) P (-0.4 < z < 0.84) = P(z < 0.84) - P(z < -0.40)

= 0.7995 - 0.3446

   = 0.4549

f.) P (z > -1.25) = 1 - P (z< -1.25)

   = 1 - 0.1056

   = 0.8954

g.) P( z < -1.49 or z > 2.50) = P( z < -1.49) + P(z > 2.5)

   = 0.0681 + 1 - 0.9938

   = 0.0743