ARE 157
Fall
2011
M. Whitney
ANALYSIS
FOR
PRODUCTIO
N
MANAGEME
NT
Homework 1, due Monday, Oct. 17th, at start of class
1. (12) Glenview Garden Products packages organic lawn fertilizer for sale to local garden
stores.
Each bag is labeled as containing 4 pounds.
In order to ensure that no customers are
shorted, the firm requires that each bag contains at least 64 ounces, with a target of 64.3 oz and
an upper limit of 64.6 oz.
The firm operates two packaging machines, and wishes to check
whether they are performing satisfactorily.
A sample from each is taken, with the following
results:
Machine A
Machine B
2
weighed 64.1
2
weighed 64.2
7
weighed 64.2
10
weighed 64.3
13
weighed 64.3
5
weighed 64.4
3
weighed 64.4
3
weighed 64.5
a. (1) After looking at the 2 samples above, one employee concluded that both machines are
operating satisfactorily, since none of the sampled bags were out of tolerance.
Explain why
this is not a satisfactory criterion for quality control purposes.
b. (8) Find the mean and sample standard deviation of each sample.
What are the lightest and
heaviest bags that are expected to occur for each machine, assuming a normal distribution?
Is each machine operating satisfactorily at present?
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 Fall '08
 WHITNEY

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