Suppose you are interested in bidding on a piece of land and you know that one other bidder is interested. The seller has announced that the highest bid in excess of $10,000 will be accepted. The other competitor's bidding price for the land will vary evenly from $10,000 to $15,000.
a) What is expected value and standard deviation of the competitor's bid?
b) What is the probability that the competitor's bid will be less than $12,000?
c) What is the range for the middle 50% of the competitor's bids?
d) Suppose that you bid $14,000. What is the probability that your bid will be accepted? (i.e. that yours will be the winning bid)
e) The competitor has hinted that he will not go higher than $13,750. What is the probability that his actual bid is above $12,200?
f) You want the probability that your bid is higher than the competitor's bid to be at least 0.95. What should you bid to ensure this?