Find the expected payback for a game in which you bet $\$ 8$ on any number from 0 to 399 . If your number comes up, you get $\$ 2000$. The expected payback is $\$ \square$. (Round to the nearest cent as needed.)

Step 1 ：Define the possible outcomes and their probabilities. In this game, there are two possible outcomes: winning $2000 with a probability of 1/400, or losing $8 with a probability of 399/400.

Step 2 ：Calculate the expected payback for each outcome by multiplying the outcome by its probability. The expected payback for winning is \(2000 \times \frac{1}{400} = 5.0\). The expected payback for losing is \(-8 \times \frac{399}{400} = -7.98\).

Step 3 ：Sum the expected paybacks for all outcomes to find the total expected payback for the game. The total expected payback is \(5.0 - 7.98 = -2.98\).

Step 4 ：Final Answer: The expected payback for the game is \(\boxed{-2.98}\).