Question

Suppose you are interested in bidding on a piece of land and you know that there are two more bidders interested. The seller announced that the highest bid above $15,000 will be accepted. Assume that the competitors can bid anywhere between $15,000 and $25,000. None of the bidders know each other.

Note: Make sure to specify the random variable and its distribution. Use the appropriate cumulative distribution table to compute the probability.

(a) Take one of the competitor bidders. What is the probability that that competitor bids within one standard deviation of the average? (10 pts)

(b) Suppose you bid $22,000. What is the probability that your bid will be accepted as the winning bid? (15 pts)

Answer 1

Let X be the random variable which takes the values between $15,000 and $25,000 randomly.

So that X follows uniform distribution with parameters a = 15000 and b = 25000

a) The formula of average of the uniform distribution is as follows:

The formula of standard deviation of the uniform distribution is as follows:

Here we want to find

b) Here we want to find P( X < 22000 ) = (22000 - 15000)/(25000 - 15000) = 7000/10000 = 0.7