Soft Drinks a Restaurant Owner Wanted to Improve the Efficiency

question 53

Essay

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.

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Definitions:

Frances Willard

A prominent 19th-century American educator, temperance reformer, and women's suffragist known for her leadership of the Woman's Christian Temperance Union (WCTU).

Charity Workers

Individuals who volunteer or are employed by nonprofit organizations to help people in need, often providing social services, aid, or relief.

Families Requesting Help

Refers to families seeking assistance, which may include financial support, social services, or resources provided by governmental or non-profit organizations.

Federal Regulatory Requirement

Rules and regulations set by federal agencies that businesses and organizations must follow to be compliant with national laws.