A manager of an apartment store reports that the time of a c

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 6minutes. 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. (PLEASE SHOW STEPS TO GET SOLUTION!)

Solution

The interval of uniform probability distribution is: [2,6].

The probability density is: 1/(6-2)=1/4

Now, P(x<3.5)=3.5/4

It takes the elevator 30 seconds to go from floor to floor.

Thu the required answer is: ½*3.5/4=0.4375