Question

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

P(z < 2) =

P(z > 1.17) =

P(−2.34 < z < 2.34) =

P(z < 1.86) =

Answer 1

Solution :

Given, a standard normal random variable with μ = 0 and standard deviation σ = 1

a) Find,  P(z < 2)

= P[Z < 2]

= 0.9772 ... ( use z table)

P(z < 2) = 0.9772

b) Find, P(z > 1.17)

= 1 - P(Z < 1.17)

= 1 - 0.8790 ........  ( use z table)

= 0.1210

P(z > 1.17) =  0.1210

c) Find,  P(−2.34 < z < 2.34)

= P(Z < 2.34) - P(Z < -2.34)

= 0.9904 - 0.0096 .......   ... ( use z table)

= 0.9808

P(−2.34 < z < 2.34) = 0.9808

d) Find,  P(z < 1.86)

= P[Z < 1.86]

= 0.9686 ... ( use z table)

P(z < 1.86) = 0.9686