Amanager 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.

The required probability is 0.6875

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 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: : min

Time to reach first floor is uniformly distributed:

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)

Hence, the required probability is 0.6875

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y