Need help with Stats homework...

From: Jen (jfern_118_at_excite.com)
Date: 06/10/04 

Date: 9 Jun 2004 19:58:51 -0700

1. The Nelson Company makes the machines that automatically dispense
soft drinks into cups. Many national fast-food chains such as
Macdonald'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 is normally distributed with a mean of 16 ounces and a
standard deviation of 0.35 ounces. A new 16 ounce cup that is being
considered for use actually holds16.7 ounces of drink.

a) Calculate the proportion of cups that will be "overpfilled" by the
automatic dispenser.
b) The company wishes to adjust the dispenser so that the overfill
percentage is no greater than 0.5%. Determine the mean required to
fulfill this wish.
c) If the mean is set at 16 ounces, calculate the standard deviation
that would be required to meet the stipulation in part (b).
d) Suppose the managers wish to have no more than 1 cup in a 1,000
overfill. What should be the mean fill setting on the dispenser to
assure that this takes place? (Assume the standard deviation stays at
0.35 ounces.)