A coladispensing machine is set to dispense a mean of 2023 l

A cola-dispensing machine is set to dispense a mean of 2.023 liters into a container labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.081 liters. What is the probability a container will have less than 2 liters?

Solution

P(X<2) = P((X-mean)/s <(2-2.023)/0.081)

=P(Z<-0.284) =0.3882 (from standard normal table)