Answer:
The required probability is 0.5
Step-by-step explanation:
Consider the provided information.
A manager of an apartment store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 4 minutes. it takes the elevator 30 seconds to go from floor to floor.
Let x denotes the waiting time.
It is given that waiting time is uniformly distributed from 2 to 4.
It is given that it takes 30 seconds to go from floor to floor.
Convert 30 seconds into minutes:
min
Time to reach first floor is uniformly distributed:
![U(2+0.5, 4+0.5)=U(2.5, 4.5)](https://tex.z-dn.net/?f=U%282%2B0.5%2C%204%2B0.5%29%3DU%282.5%2C%204.5%29)
We need to determine the probability that a hurried customer can reach the first floor in less than 3.5 minutes after pushing the elevator button on the second floor."
So we need to find ![P(Y < 3.5)](https://tex.z-dn.net/?f=P%28Y%20%3C%203.5%29)
![P(Y < 3.5) = \frac{(3.5 - 2.5)}{(4.5 - 2.5)} = 0.5](https://tex.z-dn.net/?f=P%28Y%20%3C%203.5%29%20%3D%20%5Cfrac%7B%283.5%20-%202.5%29%7D%7B%284.5%20-%202.5%29%7D%20%3D%200.5)
Hence, the required probability is 0.5