The human resources manager at a company records the length, in hours, of one shift at work, x. he creates the probability distribution below. what is the probability that a worker chosen at random works at least 8 hours?

The words at least means that the worker needs to work 8, 9 or 10 hours. We can add probabilities, so we will add .6 (for those working 8 hours), .15 (for those working 9 hours) and .08 (for those working 10 hours) to get a total probability of .83.