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:The required probability is 0.5Step-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: [tex]\frac{30}{60}=0.5[/tex] minTime to reach first floor is uniformly distributed:[tex]U(2+0.5, 4+0.5)=U(2.5, 4.5)[/tex]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  [tex]P(Y < 3.5)[/tex][tex]P(Y < 3.5) = \frac{(3.5 - 2.5)}{(4.5 - 2.5)} = 0.5[/tex]Hence, the required probability is 0.5