In a distribution with a mean of 75 and a standard deviation

In a distribution with a mean of 75 and a standard deviation of 5, what is the probability that a core will be 80 or higher?

Solution

Normal Distribution
Mean ( u ) =75
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 80) = (80-75)/5
= 5/5= 1
= P ( Z <1) From Standard Normal Table
= 0.8413                  
P(X > = 80) = (1 - P(X < 80)
= 1 - 0.8413 = 0.1587