Question

The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm. The bank has found that for all personal checking accounts the mean of all the daily balances is $900 and the standard deviation is $175. In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.

Question 1. What percentage of the bank's customers carry daily balances between $700 and $1,000? (Use 2 decimal places in your answer. Note that the answer is requested as a percent, that is, a value between 0 and 100).

Question 2.The bank is considering paying interest to customers carrying daily checking account balances in excess of a certain amount. If the bank does not want to pay interest to more than 4% of its checking account customers, what is the minimum daily balance on which it should be willing to pay interest? (Round your answer to the nearest dollar)

Answer 1

1)

µ =    900                              
σ =    175                              
we need to calculate probability for ,                                  
P (   700   < X <   1000   )                  
=P( (700-900)/175 < (X-µ)/σ < (1000-900)/175 )                                  
                                  
P (    -1.143   < Z <    0.571   )                   
= P ( Z <    0.571   ) - P ( Z <   -1.143   ) =    0.7161   -    0.1265   =    58.96%
.................

2)

µ=   900                  
σ =    175                  
proportion=   0.4                  
                      
Z value at    0.4   =   -0.25   (excel formula =NORMSINV(   0.4   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   -0.25   *   175   +   900  
X   =   856   (answer)          

please revert back for doubt