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New Process, Inc., a large mail-order supplier of women’s
Chapter 6, Problem 54E(choose chapter or problem)
Problem 54E
New Process, Inc., a large mail-order supplier of women’s fashions, advertises sameday service on every order. Recently the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95 percent of the working days. Frequent checks of the unfilled orders at the end of the day reveal that the distribution of the unfilled orders follows a Poisson distribution with a mean of two orders.
a. Has New Process, Inc., lived up to its internal goal? Cite evidence.
b. Draw a histogram representing the Poisson probability distribution of unfilled orders.
Questions & Answers
QUESTION:
Problem 54E
New Process, Inc., a large mail-order supplier of women’s fashions, advertises sameday service on every order. Recently the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95 percent of the working days. Frequent checks of the unfilled orders at the end of the day reveal that the distribution of the unfilled orders follows a Poisson distribution with a mean of two orders.
a. Has New Process, Inc., lived up to its internal goal? Cite evidence.
b. Draw a histogram representing the Poisson probability distribution of unfilled orders.
ANSWER:
Solution :
Step 1 of 2:
Let X denote the number of orders unfilled.
Then X follows a Poisson distribution with mean =2.
Then the Poisson distribution formula is
P(X=x) =
Where 2.
P(X=x) =
Our goal is:
a). We need to find New Process, Inc., lived up to its internal goal.
b). We need to draw a histogram.
a). Then the probability of fewer than 5 is
P (X fewer than 5) = P(X<5)
P (X<5) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
P (X<5) =
P (X<5) =
P (X<5) = 0.135335+0.270671+0.270671+0.180447+0.090224
P (X<5) = 0.947347
Hence this is reasonable to conclude that 94% of the working days we have fewer than 5 orders unfilled.
Therefore, the company lived up to its internal goal.