A credit card company has fraud detection service that deter

A credit card company has fraud detection service that determines if a card has any unusual activity. The company maintains a database of daily charges on a customer\'s credit card. Days when the card was inactive are excluded from the database. If a day\'s worth of charges appears unusual, the customer is contacted to make sure that the credit card has not been compromised. Use the following daily charges (round to the nearest dollar) to determine the amount the daily charges must exceed before the customer is contacted

143 166 113 188 133

90 89 98 95 112

111 79 46 20 112

70 174 68 101 212

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Sum(x) =    2220      
          
Thus,          
X =    111      
          
Setting up tables,          
x   x - X   (x - X)^2  
143   32   1024  
166   55   3025  
113   2   4  
188   77   5929  
133   22   484  
90   -21   441  
89   -22   484  
95   -16   256  
112   1   1  
111   0   0  
79   -32   1024  
98   -13   169  
46   -65   4225  
20   -91   8281  
112   1   1  
70   -41   1681  
174   63   3969  
68   -43   1849  
101   -10   100  
212   101   10201  
                      
Thus, Sum(x - X)^2 =    43148      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    20      
          
s^2 =    2270.947368      
          
Thus,          
          
s =    47.65445801      

A bill could be considered rare if it is at least 2 standard deviations from mean. [If you use a different standard, please resubmit this question.]

Thus, the critical value is

xcrit = X + 2s = 111 + 2*47.65445801

xcrit = $206.31 [ANSWER]