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:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,