813.5
814.0
814.5
815.0
815.5
816.0
816.5
Mean of Shaft Diameter
6
12
18
24
30
36
42
48
54
60
66
72
78
Day
Avg=814.992
LCL=813.700
UCL=816.284
0
1
2
3
4
5
Range of Shaft Diameter
Day
Avg=2.24
LCL=0.00
UCL=4.74
Stat 101002
Cengiz
Rahmioglu Heller
Penn ID:
37479511
STAT 101 HW
1. (a) The average process time is meaningless by itself as we don’t know the
spread of the times which is determined by the standard deviation. If σ is
small, the distribution concentrates tightly around μ whereas if σ is
large, the curve spreads farther out from μ. As a result, our decision on
which approach to adopt is heavily affected by the standard deviation.
For instance, a smaller average process time isn’t necessarily better if
the standard deviation is very large.
(b) Regular Approach:
Z
1
=(Xμ)/σ=(3035)/10=0.5
P(X<=30minutes)=0.31
New Approach:
Z
2
=(Xμ)/σ=(3040)/20=0.5
P(X<=30minutes)=0.31
Both methods are equally likely to complete an order in less than 30
minutes.
(c) If we use the Normal model, we would expect 95% of the orders to be
completed between plus or minus 2 standard deviations of the mean, a
range from 0 to 80 minutes. The lower limit is 0 minutes which indicates
that the normal model doesn’t fit this model very well. This also implies
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 Fall '08
 Heller
 Standard Deviation, shaft diameter

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