Giving a normal distribution with mean 100 and standard devi

Giving a normal distribution with mean 100 and standard deviation of 20, calculate the following probabilities

Question

Answer

P(X>130) =

P(X<90) =

P(80<X<150) =

Solution

Normal Distribution
Mean ( u ) =100
Standard Deviation ( sd )=20
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)              
P(X > 130) = (130-100)/20
= 30/20 = 1.5
= P ( Z >1.5) From Standard Normal Table
= 0.0668                  
b)
P(X < 90) = (90-100)/20
= -10/20= -0.5
= P ( Z <-0.5) From Standard Normal Table
= 0.3085  
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 80) = (80-100)/20
= -20/20 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(X < 150) = (150-100)/20
= 50/20 = 2.5
= P ( Z <2.5) From Standard Normal Table
= 0.99379
P(80 < X < 150) = 0.99379-0.15866 = 0.8351