Final answer:
The question about worker 1's times being independently distributed requires individual commute time data and statistical tests for independence, which are not provided with the given information.
Step-by-step explanation:
The question posed refers to the concept of independent distributions in statistics, a branch of mathematics. Independence in this context means that the times taken by worker 1 to complete a task on different occasions do not affect each other. However, based on the information provided, this question cannot be answered directly as there is no data regarding the individual commute times for worker 1. Instead, the information provided pertains to comparing the consistency of commute times between two workers by using their commute time variances to perform a statistical test.
To answer whether worker 1's times are independently distributed, one would typically need individual commute time data for worker 1 and possibly conduct tests such as the autocorrelation test to see if successive commute times are correlated. For the tasks related to comparing consistencies, the details suggest setting up a hypothesis test to determine if worker 1 is more consistent than worker 2 based on their commute time variances.