Find the probabilities for a standard normal random variable

Find the probabilities for a standard normal random variable Z.

a.P(Z>2.5)

b.P(1.2<Z<2.2)

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 2.5) = (2.5-0)/1
= 2.5/1 = 2.5
= P ( Z >2.5) From Standard Normal Table
= 0.0062                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1.2) = (1.2-0)/1
= 1.2/1 = 1.2
= P ( Z <1.2) From Standard Normal Table
= 0.88493
P(X < 2.2) = (2.2-0)/1
= 2.2/1 = 2.2
= P ( Z <2.2) From Standard Normal Table
= 0.9861
P(1.2 < X < 2.2) = 0.9861-0.88493 = 0.1012