question archive Times for a surgical procedure are normally distributed
Times for a surgical procedure are normally distributed
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Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 35 minutes and a standard deviation of 4 minutes, while method B has a mean of 39 minutes and a standard deviation of 2.0 minutes.
(a) Which procedure is preferred if the procedure must be completed within 35 minutes?
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Method A
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Method B
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Either Method
(b) Which procedure is preferred if the procedure must be completed within 45.0 minutes?
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Method A
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Method B
-
Either Method
(c) Which procedure is preferred if the procedure must be completed within 43 minutes?
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Method A
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Method B
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Either Method
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Ans:
a)
For method A:
z=(35-35)/4=0
P(z<=0)=0.50
For method B:
z=(35-39)/2
z=-2
P(z<=-2)=0.0228
Probability of completion within 35 minutes is higher for method A.So,
Method A should be preferred.
b)
For method A:
z=(45-35)/4=2.5
P(z<=2.5)=0.9938
For method B:
z=(45-39)/2
z=3
P(z<=3)=0.9987
Probability of completion within 45 minutes is higher for method B.So,
Method B should be preferred.
c)
For method A:
z=(43-35)/4=2
P(z<=2)=0.9773
For method B:
z=(43-39)/2
z=2
P(z<=3)=0.9773
Probability of completion within 43 minutes is equal for both methods.So,
Either method
