Answer:
b. 0.25
c. 0.05
d. 0.05
e. 0.25
Step-by-step explanation:
if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:
![P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B1%7D%7Bb-a%7D%3D%5Cfrac%7B1%7D%7B20-0%7D%20%3D0.05)
Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:
![P(X](https://tex.z-dn.net/?f=P%28X%3Cx%29%3D%5Cfrac%7Bx-a%7D%7Bb-a%7D%3D%5Cfrac%7Bx-0%7D%7B20-0%7D%3D%5Cfrac%7Bx%7D%7B20%7D)
Then, the probability that a randomly selected passenger will wait:
b. Between 5 and 10 minutes.
![P(5](https://tex.z-dn.net/?f=P%285%3Cx%3C10%29%20%3D%20P%28x%3C10%29%20-%20P%28x%3C5%29%5C%5CP%285%3Cx%3C10%29%20%3D%20%5Cfrac%7B10%7D%7B20%7D%20-%5Cfrac%7B5%7D%7B20%7D%3D0.25)
c. Exactly 7.5922 minutes
![P(7.5922)=0.05](https://tex.z-dn.net/?f=P%287.5922%29%3D0.05)
d. Exactly 5 minutes
![P(5)=0.05](https://tex.z-dn.net/?f=P%285%29%3D0.05)
e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:
![P(15](https://tex.z-dn.net/?f=P%2815%3Cx%3C25%29%3DP%2815%3Cx%3C20%29%20%5C%5CP%2815%3Cx%3C20%29%3DP%28x%3C20%29%20-%20P%28x%3C15%29%5C%5CP%2815%3Cx%3C20%29%20%3D%20%5Cfrac%7B20%7D%7B20%7D%20-%5Cfrac%7B15%7D%7B20%7D%3D0.25)