a. Suppose you bid $11,500. What is the probability that your bid will be accepted?
b. Suppose you bid $13,500. What is the probability that your bid will be accepted?
Answer:
a. 0.392
b. 0.784
Step-by-step explanation:
Given
a = 9,500 , b = 14,600
The probability density function is given by 1 divided by the interval between a and b.
f(x) = 1/(b - a)
f(x) = 1/(14,600 - 9,500)
f(x) = 1/5100
f(x) = 0.000196
a. Suppose you bid $11,500. What is the probability that your bid will be accepted?
This is given by the integration of f(x) over the interval in the probability
I.e.
P(x < 11,500) = Integral of 0.000196dx, where upper bound = 11,500 and lower bound = 9,500
Integrating 0.000196dx gives
0.000196x introducing the upper and lower bound.
We get
0.000196(11,500 - 9,500)
= 0.392
b. Suppose you bid $13,500. What is the probability that your bid will be accepted?
This is given by the integration of f(x) over the interval in the probability
I.e.
P(x < 13,500) = Integral of 0.000196dx, where upper bound = 13,500 and lower bound = 9,500
Integrating 0.000196dx gives
0.000196x introducing the upper and lower bound.
We get
0.000196(13,500 - 9,500)
= 0.784
