This is an interview questions, I am not quite sure how to solve. The question is stated as this:
Suppose that you want to buy a specific type of car, but you don't know anything about cars (you can't find the underlying quality or the real value). But dealers know about cars and they know exactly how much a car is worth (real value).
Now you are given a list of prices that different dealers bought at, but the list doesn't show which dealer bought which car. The price is normal distributed. Assume there are infinite number of dealers and the price dealers bought at is considered as the true value of the car.
If you can only bid once for each dealer, and that dealer either accept or decline your offer. Dealer will only accept your offer if and only if your offer is above their buying price.
The question is, how to bid or what price to bid, so that you minimize the loss (the price you offer minus the real value). Assume that you only need to buy one car so you can bid as many times as you want until your offer get accepted.
(Interviewer mentioned mean and standard deviation, but I still couldn't figure out.)