Suppose the force acting on a column that helps to support a

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 16.0 kips and standard deviation 1.50kips. Compute the following probabilities by standardizing and then using a standard normal curve table from the Appendix Tables. (Round your answers to four decimal places.)

(a)    

P(X 16)

P(X 19)

(c)    

P(X 10)

(d)    

P(14 X 19)

(e)    

P(|X 16| 1)

apendix table--- http://www.webassign.net/devorestat8/DevoreStat8_appendix_tables.swf

Solution

Normal Distribution
Mean ( u ) =16
Standard Deviation ( sd )=1.5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 16) = (16-16)/1.5
= 0/1.5 = 0
= P ( Z >0) From Standard Normal Table
= 0.5                  
P(X < = 16) = (1 - P(X > 16)
= 1 - 0.5 = 0.5                  

b)
P(X > 19) = (19-16)/1.5
= 3/1.5 = 2
= P ( Z >2) From Standard Normal Table
= 0.0228                  
P(X < = 19) = (1 - P(X > 19)
= 1 - 0.0228 = 0.9772                  

c)
P(X < 10) = (10-16)/1.5
= -6/1.5= -4
= P ( Z <-4) From Standard Normal Table
= 0                  
P(X > = 10) = (1 - P(X < 10)
= 1 - 0 = 1                  

d)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 14) = (14-16)/1.5
= -2/1.5 = -1.3333
= P ( Z <-1.3333) From Standard Normal Table
= 0.09121
P(X < 19) = (19-16)/1.5
= 3/1.5 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(14 < X < 19) = 0.97725-0.09121 = 0.886