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The manager of the local National Video Store sells videocassette recorders at discount prices. If
the store does not have a video recorder in stock when a customer wants to buy one, it will lose the
sale because the customer will purchase a recorder from one of the many local competitors. The
problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet
all demand is excessively high. The manager has determined that if 85% of customer demand for
recorders can be met, then the combined cost of lost sales and inventory will be minimized. The
manager has estimated that monthly demand for recorders is normally distributed, with a mean of
175 recorders and a standard deviation of 55. Determine the number of recorders the manager
should order each month to meet 85% of customer demand.
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The problem talks about a normal distribution curve, which has the mean of 175 and the standard
deviation of 55.
They want you find the score x such that the area under this given normal curve on the left of this score is 0.85.
Use a standard calculator like TI-84/87 and its standard function invNorm().
Its format is x = invNorm(area, mean, SD).
The function will return the value invNorm(0.85, 175, 55) = 232.
So, x = 232 is the number of recorders the manager should keep in the store
at the beginning of each month to satisfy 85% of customer demand during a month.
It is the ANSWER to the problem's question.
The problem is solved.
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Notice that the problem's question is posed incorrectly.
It asks "how many recorders the manager should order each month",
while the correct question should ask "how many recorders the manager should have
at the storage at the beginning of each month".