Problem #PRU-65348

Problem

The figure shows a payment order to pay an electricity bill to some power supply company for March 2013.

Every month, the client sends the company the testimony of a three-tariff meter installed her the apartment. From the indications for the current month, the corresponding indications for the previous month are subtracted, and the actual monthly expenditure is obtained for each of the three tariff zones (peak, night, inter-peak). Then the expense for each zone is multiplied by the price of one kilowatt-hour in this zone. Adding the received amounts, the client receives the total amount of payment for a month. In this example, the customer will pay £660.72.

The company maintains a record of electricity consumption and payment, using the data received from the customer. The problem is that the company sometimes confuses the six numbers obtained, rearranging them in an arbitrary order, however, it ensures that the current reading remains greater than the previous one. As a result, the calculation of the company may be flawed. If the company believes that the client must pay more than she has paid, the company requires additional payment.

Using the data from the receipt shown, find:

a) the maximum possible amount of surcharge for March 2013, which the company will require from the client;

b) the mathematical expectation of the difference between the amount that the company calculates and the amount paid by the client.