Respuesta :
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.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
This means that [tex]a = 10400, b = 15400[/tex]
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
[tex]P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32[/tex]
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
[tex]P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72[/tex]
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.
