Question

Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 35 minutes and a standard devlation of 3 minutes, while method Bhas a mean of 39 minutes and a standard devlation of 1.5 minutes. (a) Which procedure is preferred If the procedure must be completed within 34 minutes? O Method A Method B Either Method (b) Which procedure is preferred If the procedure must be completed within 40.0 minutes? Elther Method MethodA O Method B (c) Which procedure Is preferred If the procedure must be completed within 43 minutes? O Method A Method B Either Method

Answer 1

A)

method A-

µ =    35              
σ =    3              
left tailed                  
P( X ≤    34   )          
                  
Z =(X - µ ) / σ = (   34   -   35   ) /    3
Z =    -0.333              
P(X ≤   34   ) = P(Z ≤   -0.333   ) =   0.3694

excel formula for probability from z score is =NORMSDIST(Z)                  
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method B-

µ =    39              
σ =    1.5              
left tailed                  
P( X ≤    34   )          
                  
Z =(X - µ ) / σ = (   34   -   39   ) /    1.5
Z =    -3.333              
P(X ≤   34   ) = P(Z ≤   -3.333   ) =   0.0004
excel formula for probability from z score is =NORMSDIST(Z)                  

so,method A has more chance of of completing procedure within 34 minutes

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B)

method A-

µ =    35              
σ =    3              
left tailed                  
P( X ≤    40   )          
                  
Z =(X - µ ) / σ = (   40   -   35   ) /    3
Z =    1.667              
P(X ≤   40   ) = P(Z ≤   1.667   ) =   0.9522
excel formula for probability from z score is =NORMSDIST(Z)

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method B

µ =    39              
σ =    1.5              
left tailed                  
P( X ≤    40   )          
                  
Z =(X - µ ) / σ = (   40   -   39   ) /    1.5
Z =    0.667              
P(X ≤   40   ) = P(Z ≤   0.667   ) =   0.7475
excel formula for probability from z score is =NORMSDIST(Z)                  
  

so,method A has more chance of of completing procedure within 40 minutes

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C)

method A-

µ =    35              
σ =    3              
left tailed                  
P( X ≤    43   )          
                  
Z =(X - µ ) / σ = (   43   -   35   ) /    3
Z =    2.667              
P(X ≤   43   ) = P(Z ≤   2.667   ) =   0.9962
excel formula for probability from z score is =NORMSDIST(Z)  

-------------------------

method B

µ =    39              
σ =    1.5              
left tailed                  
P( X ≤    43   )          
                  
Z =(X - µ ) / σ = (   43   -   39   ) /    1.5
Z =    2.667              
P(X ≤   43   ) = P(Z ≤   2.667   ) =   0.9962
excel formula for probability from z score is =NORMSDIST(Z)                  

so,method A and method B has same chance of of completing procedure within 40 minutes

so, answer is either method