Question

The waiting time at a bus stop for the next bus to arrive is uniformly distributed between 0 and 20 minutes.

(a). Find the probability that the waiting time is less than 8 minutes.
The probability that the waiting time is less than 8 minutes is

Answer 1

The probability that the waiting time is less than 8 minutes is 0.2.

Step-by-step explanation:

To find the probability that the waiting time is less than 8 minutes, we need to calculate the area under the probability density function curve up to the value of 8.

Since the waiting time is uniformly distributed between 0 and 20 minutes, the probability density function is a rectangle with base 20 and height 1/20. The area of the rectangle is given by base times height, so the probability is (8/20) x (1/20) = 0.2.