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 < 0.2) =  

(b) P(z < -0.2) =  

(c) P(0.40 < z < 0.86) =  

(d) P(-0.86 < z < -0.40) =  

(e) P(-0.40 < z < 0.86) =  

(f) P(z > -1.24) =  

(g) P(z < -1.5 or z > 2.50) =

Answer 1

Solution :

Given that,  

Using standard normal table ,

(a)

P(z < 0.2) = 0.5793

(b)

P(z < -0.2) = 0.4207

(c)

P(0.40 < z < 0.86)

= P(z < 0.86) - P(z < 0.40)

= 0.8051 - 0.6554

= 0.1497

P(0.40 < z < 0.86) = 0.1497

(d)

P(-0.86 < z < -0.40)

= P(z < -0.40) - P(z < -0.86)

= 0.3446 - 0.1949

= 0.1497

P(-0.86 < z < -0.40) = 0.1497

(e)

P(-0.40 < z < 0.86)

= P(z < 0.86) - P(z < -0.40)

= 0.8051 - 0.3446

= 0.4605

P(-0.40 < z < 0.86) = 0.4605

(f)

P(z > -1.24) = 1 - P(z < -1.24) = 1 - 0.1075 = 0.8925

(g)

P(z < -1.5 or z > 2.50)

= 1 - P(z < -1.5) - P(z < 2.50)

= 1 - P(z < 2.50) - P(z < -1.5)

= 1 - P (0.9938 - 0.0668)

= 1 - 0.927

= 0.073

P(z < -1.5 or z > 2.50) = 0.073