Given that z is a standard normal random variable compute th

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).

(4)

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X <= -1) = (-1-0)/1
= -1/1= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587                  
b)
P(X >= -1.5) = (-1.5-0)/1
= -1.5/1 = -1.5
= P ( Z >-1.5) From Standard Normal Table
= 0.9332                  
c)
P(X >= 2.5) = (2.5-0)/1
= 2.5/1 = 2.5
= P ( Z >2.5) From Standard Normal Table
= 0.0062