Homework Chapter 6
Question 2, 6.1.5
HW Score: $1.96 \%, 1$ of 51 points
Points: 0 of 1
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 5 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
(Simplify your answer. Round to three decimal places as needed.)

Step 1 ：The waiting times are uniformly distributed between 0 and 5 minutes. This means that the probability of any given waiting time within this range is the same. The total range of waiting times is 5 minutes.

Step 2 ：The question asks for the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. This means we need to find the proportion of the total range that is greater than 2.25 minutes.

Step 3 ：This can be calculated by subtracting 2.25 from the total range of 5 minutes, and then dividing by the total range.

Step 4 ：\(total\_range = 5\)

Step 5 ：\(waiting\_time = 2.25\)

Step 6 ：\(probability = \frac{total\_range - waiting\_time}{total\_range}\)

Step 7 ：\(probability = \frac{5 - 2.25}{5} = 0.55\)

Step 8 ：The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is 0.55 or 55%. This is the proportion of the total range of waiting times that is greater than 2.25 minutes.

Step 9 ：Final Answer: The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is \(\boxed{0.55}\) or \(\boxed{55\%}\).