Question

Consider a standard normal random variable with μ = 0 and standard deviation σ = 1. (Round your answers to four decimal places.)

(a)    

P(z < 2) =

(b)    

P(z > 1.13) =

(c)    

P(−2.39 < z < 2.39) =

(d)    

P(z < 1.88) =

Answer 1

Solution :

z has standard normal distribution.

μ = 0 and standard deviation σ = 1

Using Standard Normal Table of probabilitis

Answers :

• (a) P(z < 2) = 0.9772
• (b) P(z > 1.13) = 0.1292
• (c)P(−2.39 < z < 2.39) = 0.9832
• (d)  P(z < 1.88) = 0.9699

See the answers with all detailed calculation and standard normal table below,

(a)    

P(z < 2) = 0.9772

(b)    

P(z > 1.13) = 1 - P( z < 1.13) = 1-0.8708 = 0.1292

(c)    

P(−2.39 < z < 2.39) = P(z<2.39)-P(z<-2.39) = 0.9916 - 0.0084 = 0.9832

(d)    

P(z < 1.88) = 0.9699