Question

Suppose ARB Bank is reviewing its service charges and interest payment policies on current accounts. Suppose further that ARB has found that the average daily balance on personal current accounts is GH¢350.00, with a standard deviation of GH¢160.00. In addition, the average daily balances have been found to follow a normal distribution;
What percentage of customers carries a balance of GH¢100 or lower?
What percentage of customers carries a balance of GH¢500 or lower?
What percentage of current account customers carries average daily balances exactly equal to GH¢500?
What percentage of customers maintains account balance between GH¢100 and GH¢500?

Answer 1

$P(X\le100)=P(Z<\frac{100-350}{160})=P(Z<-1.56)=0.0594=5.94\%.$

$P(X\le500)=P(Z<\frac{500-350}{160})=P(Z<0.94)=0.8264=82.64\%.$

$P(X=500)=0.$

$P(100<X<500)=P(\frac{100-350}{160}<Z<\frac{500-350}{160})=P(-1.56<Z<0.94)=$

$=P(Z<0.94)-P(Z<-1.56)=0.8264-0.0594=0.767=76.7\%.$