Answer:
a) 0.32 = 32% probability that your bid will be accepted
b) 0.72 = 72% probability that your bid will be accepted
c) An amount in excess of $15,400.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
![P(X \leq x) = \frac{x - a}{b-a}](https://tex.z-dn.net/?f=P%28X%20%5Cleq%20x%29%20%3D%20%5Cfrac%7Bx%20-%20a%7D%7Bb-a%7D)
Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
This means that ![a = 10400, b = 15400](https://tex.z-dn.net/?f=a%20%3D%2010400%2C%20b%20%3D%2015400)
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
You will win if the competitor bids less than 12000. So
![P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2012000%29%20%3D%20%5Cfrac%7B12000%20-%2010400%7D%7B15400%20-%2010400%7D%20%3D%200.32)
0.32 = 32% probability that your bid will be accepted
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
You will win if the competitor bids less than 14000. So
![P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2014000%29%20%3D%20%5Cfrac%7B14000%20-%2010400%7D%7B15400%20-%2010400%7D%20%3D%200.72)
0.72 = 72% probability that your bid will be accepted
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
His bid is uniformly distributed between $10,400 and $15,400.
So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.