Question

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. If it takes the elevator 30 seconds to go from floor to floor, find 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."

Answer 1

The required probability is 0.5

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:
`(30)/(60)=0.5` min

Time to reach first floor is uniformly distributed:

`U(2+0.5, 4+0.5)=U(2.5, 4.5)`

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)`

`P(Y < 3.5) = ((3.5 - 2.5))/((4.5 - 2.5)) = 0.5`

Hence, the required probability is 0.5