Determine the probability that the standard normal random va

Determine the probability that the standard normal random variable will assume a single value between -1.42 and 0.75.

Find the probability that a single value of the standard normal random variable will be between zero and 1.52.

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -1.42) = (-1.42-0)/1
= -1.42/1 = -1.42
= P ( Z <-1.42) From Standard Normal Table
= 0.0778
P(X < 0.75) = (0.75-0)/1
= 0.75/1 = 0.75
= P ( Z <0.75) From Standard Normal Table
= 0.77337
P(-1.42 < X < 0.75) = 0.77337-0.0778 = 0.6956                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0) = (0-0)/1
= 0/1 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 1.52) = (1.52-0)/1
= 1.52/1 = 1.52
= P ( Z <1.52) From Standard Normal Table
= 0.93574
P(0 < X < 1.52) = 0.93574-0.5 = 0.4357