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 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 holds 16.7 ounces of drink.

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 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 holds 16.7 ounces of drink.

a). Calculate the proportion of cups that will be “over-filled” 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). Which of the two procedures described in parts (b) and (c) do you prefer? Explain carefully.

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