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 0 to 4 minutes. If it takes the elevator 15 seconds to go from floor to floor, find the probability that a hurried customer can reach the first floor in less than 3 minutes after pushing the elevator button on the second floor.

Answer 1

The required probability is 0.6875

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 0 to 4 minutes. The elevator 15 seconds to go from floor to floor,

Let x denotes the waiting time.

It is given that waiting time is uniformly distributed from 0 to 4.

It is given that it takes 15 seconds to go from floor to floor.

Convert 15 seconds into minutes: :
`(15)/(60)=0.25` min

Time to reach first floor is uniformly distributed:

`U(0+0.25, 4+0.25)=U(0.25, 4.25)`

We need to determine the probability that a hurried customer can reach the first floor in less than 3 minutes after pushing the elevator button on the second floor."

So we need to find P(Y < 3)

`P(Y < 3) = ((3 - 0.25))/((4.25 - 0.25)) =0.6875`

Hence, the required probability is 0.6875