A cola-dispensing machine is set to dispense a mean of 2.02 liters into a bottle labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters. a. What is the probability a bottle will contain between 2.00 and 2.03 liters? b. What is the probability a bottle will contain less than 2 liters? c. 2% of the containers will contain how much cola or more?

Answer:Step-by-step explanation:Given that a  cola-dispensing machine is set to dispense a mean of 2.02 liters into a bottle labeled 2 liters. Std deviation =0.015 litresX- litres contained in a bottle is N(2.02, 0.15)Z score is obtained as [tex]z=\frac{x-2.02}{0.015}[/tex]a) probability a bottle will contain between 2.00 and 2.03 liters=P(2<x<2.03) = P(-1.33<Z<2) = 0.4082+0.4772=0.8854b) P(X<2) = P(Z<-1.33) =0.5-0.4082 = 0.0918c) 2% of containers|z|<0.11X lies between 0.6883 and 3.352 l