The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes?
A) 0.4706
B) 0.5294
C) 0.6000
D) 0.7059

Question

Quizplus · Accepted Answer

- Two minutes is equal to 120 seconds.
- The probability of waiting less than 120 seconds can be found by calculating the area of the rectangle between 30 and 120 on the x-axis and 0 and 1 on the y-axis, since the waiting time is uniformly distributed.
- The total area under the density curve is 1.
- The width of the rectangle is 90 (120-30) and the height is 1/170 (1/170 is the height of uniform density curve since it is a constant).
- Therefore, the area of the rectangle is (90*1/170) = 0.5294.
- Hence, the probability that a rider waits less than two minutes is 0.5294.

The Waiting Time at an Elevator Is Uniformly Distributed Between