Answer:
a) The expected arrival time is 2.25 minutes.
b) 25.88% probability that an elevator arrives in less than 1.1 minutes
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 < x) = \frac{x - a}{b-a}](https://tex.z-dn.net/?f=P%28X%20%3C%20x%29%20%3D%20%5Cfrac%7Bx%20-%20a%7D%7Bb-a%7D)
The expected value of the uniform distribution is given by:
![M = \frac{a+b}{2}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Ba%2Bb%7D%7B2%7D)
The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4.5 minutes.
This means that ![a = 0, b = 4.5](https://tex.z-dn.net/?f=a%20%3D%200%2C%20b%20%3D%204.5)
a. Calculate the expected arrival time. (Round your answer to 2 decimal place.)
![M = \frac{a+b}{2} = \frac{0 + 4.5}{2} = 2.25](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Ba%2Bb%7D%7B2%7D%20%3D%20%5Cfrac%7B0%20%2B%204.5%7D%7B2%7D%20%3D%202.25)
The expected arrival time is 2.25 minutes.
b. What is the probability that an elevator arrives in less than 1.1 minutes
![P(X < 1.1) = \frac{1.1 - 0}{4.25 - 0} = 0.2588](https://tex.z-dn.net/?f=P%28X%20%3C%201.1%29%20%3D%20%5Cfrac%7B1.1%20-%200%7D%7B4.25%20-%200%7D%20%3D%200.2588)
25.88% probability that an elevator arrives in less than 1.1 minutes