Soft drinks A restaurant owner wanted to improve the efficiency of his employees. One way he tried to do this was to buy a machine that will automatically dispense 16 oz. of soda into a glass rather than have the employee hold the button on the dispenser. The actual amount dispensed by the machine can be represented by the model N(16.2, 0.3)
a. Draw and clearly label the model.
b. The sales representative who sold him the machine said, "95% of the glasses you fill with soda will fall between _________ and _________." Fill in the blanks based on the normal model, then comment on this claim.
c. What is the 3rd quartile of amounts dispensed?
d. If a glass will actually hold 16.7 oz. of soda, what percent of the time would you expect the glass to overflow?
e. The manufacturer wants to reduce the overflow rate to only 1%. Assuming the mean amount dispensed will stay the same, what standard deviation must they achieve?
f. Briefly explain what that change in standard deviation means in this context.
g. A competing manufacturer says that not only will 98% of their glasses be safe from overflowing, but 70% will have more than 16 oz., reducing customer complaints. What Normal model parameters is that manufacturer claiming? Show your work.

Question

Soft drinks A restaurant owner wanted to improve the efficiency of his employees. One way he tried to do this was to buy a machine that will automatically dispense 16 oz. of soda into a glass rather than have the employee hold the button on the dispenser. The actual amount dispensed by the machine can be represented by the model N(16.2, 0.3)
a. Draw and clearly label the model.  
b. The sales representative who sold him the machine said, "95% of the glasses you fill with soda will fall between _________ and _________." Fill in the blanks based on the normal model, then comment on this claim.
c. What is the 3rd quartile of amounts dispensed?
d. If a glass will actually hold 16.7 oz. of soda, what percent of the time would you expect the glass to overflow?
e. The manufacturer wants to reduce the overflow rate to only 1%. Assuming the mean amount dispensed will stay the same, what standard deviation must they achieve?
f. Briefly explain what that change in standard deviation means in this context.
g. A competing manufacturer says that not only will 98% of their glasses be safe from overflowing, but 70% will have more than 16 oz., reducing customer complaints. What Normal model parameters is that manufacturer claiming? Show your work.

Quizplus · Accepted Answer

The Answer of Soft drinks A restaurant owner wanted to improve the efficiency of his employees. One way he tried to do this was to buy a machine that will automatically dispense 16 oz. of soda into a glass rather than have the employee hold the button on the dispenser. The actual amount dispensed by the machine can be represented by the model N(16.2, 0.3)
a. Draw and clearly label the model.  
b. The sales representative who sold him the machine said, "95% of the glasses you fill with soda will fall between _________ and _________." Fill in the blanks based on the normal model, then comment on this claim.
c. What is the 3rd quartile of amounts dispensed?
d. If a glass will actually hold 16.7 oz. of soda, what percent of the time would you expect the glass to overflow?
e. The manufacturer wants to reduce the overflow rate to only 1%. Assuming the mean amount dispensed will stay the same, what standard deviation must they achieve?
f. Briefly explain what that change in standard deviation means in this context.
g. A competing manufacturer says that not only will 98% of their glasses be safe from overflowing, but 70% will have more than 16 oz., reducing customer complaints. What Normal model parameters is that manufacturer claiming? Show your work.

Soft Drinks a Restaurant Owner Wanted to Improve the Efficiency