Credit Card Fraud Detection: You are tasked with setting up a fraudulent purchase alert program for a bank.

1. Credit Card Fraud Detection: You are tasked with setting up a fraudulent purchase alert program for a bank. The idea is to send customers a verification text message whenever a large purchase is made to ensure the purchase wasn't fraudulent. For each customer you have access to their purchase history only in the form of their mean purchase amount and the standard deviation of their purchase amounts. You certainly don't want to annoy your customers with text message alerts every time they buy a coffee--but you also want to ensure how capture any costly fraudulent purchases.

Assume you are considering a customer with an average purchase of 5 dollars with a standard deviation of 5 dollars.

•  Is this distribution of your purchase amounts likely to be symmetric? What do you expect this distribution (histogram of purchase prices) to look like roughly?
•  If you want to notify this customer for no more than 25% of the purchases what should you set as the threshold price for sending a text message?
•  Discuss how this procedure could be improved upon if you are given the entire purchase history (prices of all purchases made) for each customer. What are the disadvantages of this procedure?