The weight of the cereal in a box is normal a random variabl

The weight of the cereal in a box is normal a random variable with mean 12.15 and standard deviation 0.2 What percentage of the boxes have contents that weight under 12 ? If the manufacturer claims that there are 12 in a box, does the percentage you just cause concern?

Solution

Normal Distribution
Mean ( u ) =12.15
Standard Deviation ( sd )=0.2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 12) = (12-12.15)/0.2
= -0.15/0.2= -0.75
= P ( Z <-0.75) From Standard Normal Table
= 0.2266                  
Approximately 22.66% are below 12 ounces