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

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: $\frac{30}{60}=0.5$ 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  $P(Y < 3.5)$

$P(Y < 3.5) = \frac{(3.5 - 2.5)}{(4.5 - 2.5)} = 0.5$

Hence, the required probability is 0.5