Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time less than 0.75 minutes.

Answer 1

The probability that a randomly selected passenger has a waiting time less than 0.75 minutes when the waiting times are uniformly distributed between 0 and 7 minutes is approximately 10.71%.

Step-by-step explanation:

To find the probability that a randomly selected passenger has a waiting time less than 0.75 minutes on a subway where the waiting times are uniformly distributed between 0 and 7 minutes, you use the properties of the uniform distribution.

The formula for the probability of the uniform distribution is:

Probability (A < X < B) = (B - A) / (Total length of the distribution)

For this case:

• A = 0 (since we are looking for the probability of less than 0.75 minutes)
• B = 0.75
• Total length of the distribution = 7 minutes

Therefore, the probability that a passenger waits less than 0.75 minutes is:

Probability = (0.75 - 0) / 7

= 0.75 / 7

<= 0.1071 (approx)

So, there is approximately a 10.71% chance that a passenger will wait less than 0.75 minutes.