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 $25,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $25,000 and $30,000. (a) Suppose you bid $27,000. What is the probability that your bid will be accepted? (b) Suppose you bid $28,000. What is the probability that your bid will be accepted? (c) What amount should you bid in dollars to maximize the probability that you get the property?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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11.
DETAILS
ASWSBE14 6.E.007.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
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 $25,000 will be accepted. Assume that the
competitor's bid x is a random variable that is uniformly distributed between $25,000 and $30,000.
(a) Suppose you bid $27,000. What is the probability that your bid will be accepted?
(b) Suppose you bid $28,000. What is the probability that your bid will be accepted?
(c) What amount should you bid in dollars to maximize the probability that you get the property?
$
(d) Suppose you know someone who is willing to pay you $31,000 for the property.
What is the expected profit in dollars if you bid the amount given in part (c)?
$
Find a bid in dollars which produces a greater expected profit than bidding the amount given in part (c). (If an answer does not exist, enter DNE.)
$
Would you consider bidding less than the amount in part (c)? Why or why not?
Yes. There is a bid which gives a greater expected profit than the bid given in part (c), and thus a higher expected profit is possible with a bid smaller than the amount in part (c).
No. The bid which maximizes the expected profit is the amount given in part (c), thus it does not make sense to place a smaller bid.
Transcribed Image Text:11. DETAILS ASWSBE14 6.E.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 $25,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $25,000 and $30,000. (a) Suppose you bid $27,000. What is the probability that your bid will be accepted? (b) Suppose you bid $28,000. What is the probability that your bid will be accepted? (c) What amount should you bid in dollars to maximize the probability that you get the property? $ (d) Suppose you know someone who is willing to pay you $31,000 for the property. What is the expected profit in dollars if you bid the amount given in part (c)? $ Find a bid in dollars which produces a greater expected profit than bidding the amount given in part (c). (If an answer does not exist, enter DNE.) $ Would you consider bidding less than the amount in part (c)? Why or why not? Yes. There is a bid which gives a greater expected profit than the bid given in part (c), and thus a higher expected profit is possible with a bid smaller than the amount in part (c). No. The bid which maximizes the expected profit is the amount given in part (c), thus it does not make sense to place a smaller bid.
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