Question

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $9,800 will be accepted. Assume that the competitor's bid is a random variable that is uniformly distributed between $9,800 and $14,800 a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)? b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)? c. What amount should you bid to maximize the probability that you get the property? d. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (e) but a friend suggests you bid $12,900. Which bid will give you the larger expected profit? - Select your answer What is the expected profit for this bid (to 2 decimals)? Check My Work remainine Choose the correct option. - Select your answer - 1 b. What is the probability that the random variable will assume a value between 45 and 55 (to 4 decimals)? c. What is the probability that the random variable will assume a value between 40 and 60 (to 4 decimals)?

Answer 1

a. The probability that your bid of $12,000 will be accepted is 0.44. b. The probability that your bid of $14,000 will be accepted is 0.84. c. The amount you should bid to maximize the probability of getting the property is $14,800. d. The bid of $14,000 will give you the larger expected profit with an expected profit of $2,640.

Step-by-step explanation:

a. To find the probability that your bid will be accepted, we need to find the probability that the competitor's bid is less than $12,000. Since the competitor's bid is uniformly distributed between $9,800 and $14,800, the probability can be calculated as the ratio of the difference between $9,800 and $12,000 to the total difference between $9,800 and $14,800.

The probability is calculated as follows:

(12,000 - 9,800) / (14,800 - 9,800) = 0.44

So, the probability that your bid will be accepted is 0.44.

b. To find the probability that your bid will be accepted when you bid $14,000, we need to find the probability that the competitor's bid is less than $14,000. Using the same method as before, we can calculate the probability as:

(14,000 - 9,800) / (14,800 - 9,800) = 0.84

So, the probability that your bid will be accepted is 0.84.

c. To maximize the probability of getting the property, you should bid the highest amount possible within the range of $9,800 to $14,800. The highest bid within this range is $14,800, so that is the amount you should bid to maximize the probability.

d. To determine which bid will give you the larger expected profit, we need to calculate the expected profit for each bid. The expected profit is calculated by multiplying the probability of winning by the difference between the bid and the cost, and then subtracting the cost of bidding.

For the bid of $12,900:

(0.44 * (16,000 - 12,900)) - 12,900 = 1,324

For the bid of $12,900, the expected profit is $1,324.

For the bid of $12,900:

(0.84 * (16,000 - 12,900)) - 14,000 = 2,640

For the bid of $14,000, the expected profit is $2,640.

Therefore, the bid of $14,000 will give you the larger expected profit.