Dr. V.R. Bencivenga
Economics 329
PRACTICE ASSIGNMENT #7A: SAMPLING
For each question (except problem 1), give
(i)
the sample statistic,
(ii)
the sampling distribution of the sample
statistic, and
(iii)
the reason why the sample statistic has this sampling distribution, based on the assumptions of
the question.
This information is necessary to receive credit.
Note:
If the tabulated c.d.f. you have is not sufficiently detailed to give a final answer on an exam, just write
down the probability you would look up if you had a more detailed table.
1.
(Review of the normal probability model)
Suppose that you are the manager of a plant that manufactures disk dr
ives for PC’
s.
One of your
machines produces a component part for these drives.
The
width
of this part is important to operation
of the disk drive.
If width is below 3.995 millimeters (mm) or above 4.005 mm, the drive will not work
properly and the part must be modified at a cost of $10.40 before it can be used.
The machine is set to
produce parts with a width of 4 mm, but it is not perfectly accurate.
Widths of parts are normally
distributed with mean 4 mm, and a variance that depends on the speed at which the machine producing
them is operated.
There are two speeds, high and low.
At the high speed, the machine is less precise.
If
the machine is run at a low speed, the variance is.00000361, and if it is run at a high speed, the variance
is .00000676.
Of course, the high speed means more parts can be produced per day, thus lowering the average cost of
manufacturing a disk drive.
If the part is produced at a high speed, the cost of the disk drive is $20.45,
while if the part is produced at a low speed, the cost of the disk drive is $20.75.
(This does not include
the cost of modifying a toowide or toonarrow part when necessary.)
The question you face as plant manager is whether you should run the machine at the high speed or the
low speed.
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 Spring '12
 BENCIVENGA
 Economics

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