Final answer:
A lone worker waiting for a train may have varying waiting times. The waiting times can be represented by a uniform distribution. The probabilities of waiting less than one minute and between three and four minutes can be calculated using the area under the probability density function (PDF) curve.
Step-by-step explanation:
A lone worker waiting for a train requires a certain amount of time before the train arrives. The waiting time can be represented by a uniform distribution, where the train is expected to arrive every eight minutes. To find the probability that the worker waits less than one minute, you need to calculate the area under the probability density function (PDF) curve from 0 to 1. To find the probability that the worker waits between three and four minutes, you need to calculate the area under the PDF curve from 3 to 4.
To find the probability that sixty percent of commuters wait more than a certain time for the train, you would need more information or specific values to calculate the probability.