The waiting times between a subway to Podger schedule and the arrival of the passenger on uniformly distributed between zero and nine minutes find the probability that a randomly selected passenger has been waiting greater than 3.25 minutes
(9-3.25)/9 = ?
.638
To find the probability that a randomly selected passenger has been waiting for greater than 3.25 minutes, we need to calculate the proportion of the total time interval that corresponds to waiting times greater than 3.25 minutes.
Since the waiting times are uniformly distributed between zero and nine minutes, we can represent this as a continuous uniform distribution.
The continuous uniform distribution is characterized by two parameters: the minimum value (a) and the maximum value (b) of the interval.
In this case, the minimum value (a) is zero and the maximum value (b) is nine.
To calculate the probability that a randomly selected passenger has been waiting for greater than 3.25 minutes, we can subtract the cumulative probability at 3.25 minutes from 1.
Let's perform the calculations step by step:
1. Calculate the range of the interval: range = b - a = 9 - 0 = 9.
2. Calculate the cumulative probability at 3.25 minutes:
cumulative probability = (3.25 - a) / range = (3.25 - 0) / 9 = 3.25 / 9 ≈ 0.3611.
3. Calculate the probability of waiting greater than 3.25 minutes:
probability = 1 - cumulative probability = 1 - 0.3611 ≈ 0.6389.
Therefore, the probability that a randomly selected passenger has been waiting for greater than 3.25 minutes is approximately 0.6389 or 63.89%.