The life expectancy of a particular brand of tire is normall

The life expectancy of a particular brand of tire is normally distributed with a population mean of 40,000 and a population standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

Solution

Mean ( u ) =40000
Standard Deviation ( sd )=5000
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 30000) = (30000-40000)/5000
= -10000/5000= -2
= P ( Z <-2) From Standard Normal Table
= 0.0228                  
P(X > = 30000) = (1 - P(X < 30000)
= 1 - 0.0228 = 0.977 ~ 97.725%