stat 8 hw

stat 8 hw - Stat 101-002 Rahmioglu Heller 37479511 Cengiz...

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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 101-002 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 =(X-μ)/σ=(30-35)/10=-0.5 P(X<=30minutes)=0.31 New Approach: Z 2 =(X-μ)/σ=(30-40)/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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stat 8 hw - Stat 101-002 Rahmioglu Heller 37479511 Cengiz...

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