The yield strength is mu 43 sigma 45 What is the probabili

The yield strength is:

mu = 43

sigma = 4.5

What is the probability that the yield strength is at most 40?

What is the probability that the yield strength is greater than 60?

What yield strength value separates the strongest 75% from the others?

Solution

Normal Distribution
Mean ( u ) =43
Standard Deviation ( sd )=4.5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 40) = (40-43)/4.5
= -3/4.5 = -0.6667
= P ( Z >-0.667) From Standard Normal Table
= 0.7475                  
P(X < = 40) = (1 - P(X > 40)
= 1 - 0.7475 = 0.2525                  
b)
P(X > 60) = (60-43)/4.5
= 17/4.5 = 3.7778
= P ( Z >3.778) From Standard Normal Table
= 0.0001                  
c)
P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 43/4.5 ) = 0.75
That is, ( x - 43/4.5 ) = 0.67
--> x = 0.67 * 4.5 + 43 = 46.033