The Nelson Company makes the machines that automatically dispense soft drinks into cups. Many national fast food chains such as McDonald's and Burger King use these machines. A study by the company shows that the actual volume of soft drink that goes into a 16-ounce cup per fill can be approximated by a normal model with mean 16 ounces and standard deviation 0.35 ounces.
A new 16-ounce cup that is being considered for use actually holds 16.7 ounces of drink.
a. What is the probability that a new cup will overflow when filled by the automatic dispenser?
b. The company wishes to adjust the dispenser so that the probability that a new cup will overflow is .006. At what value should the mean amount dispensed by the machine be set to satisfy this wish? 2 ounces. (Use 2 decimal places in your answer and use 0.35 ounces for the standard deviation).