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Please solve the following questions related to Chapter 7 and 8: 1. A bank has kept records of the checking balances of its 4

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Answer #1

a)

0.05N = 4000*0.05=200

n<0.05N, so, population finite correction factor will not be used here,

µ =    300                                      
σ =    48                                      
n=   144                                      
                                          
X =   309                                      
                                          
Z =   (X - µ )/(σ/√n) = (   309   -   300   ) / (    48   / √   144   ) =   2.250  
                                          
P(X ≥   309   ) = P(Z ≥   2.25   ) =   P ( Z <   -2.250   ) =    0.0122           (answer)

b)

we need to calculate probability for ,                                          
293   ≤ X ≤    307                                  
X1 =    293   ,    X2 =   307                          
                                          
Z1 =   (X1 - µ )/(σ/√n) = (   293   -   300   ) / (   48   / √   144   ) =   -1.75  
Z2 =   (X2 - µ )/(σ/√n) = (   307   -   300   ) / (   48   / √   144   ) =   1.75  
                                          
P (   293   < X <    307   ) =    P (    -1.75   < Z <    1.75   )       
                                          
= P ( Z <    1.75   ) - P ( Z <   -1.75   ) =    0.960   -    0.040   =    0.9199       (answer)

c)

N=2000

0.05N = 0.05*2000 = 100

n>0.05N , so, population finite correction factor will be used here,

n=144

standard error , SE = σ/√n * √((N-n)/(N-1)) =   3.854


we need to calculate probability for ,                                      
P (   296   < X <   305   )                      
=P( (296-300)/3.854 < (X-µ)/SE < (305-300)/3.854 )                                      
                                      
P (    -1.038   < Z <    1.297   )                       
= P ( Z <    1.297   ) - P ( Z <   -1.038   ) =    0.9027   -    0.1497   =    0.7530   (answer)

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