Are you confusing precision with accuracy?
The idea behind Agile estimation is to come up with a number that is good enough, not a number that is exact. That is why using story points for backlog item estimation is a best practice; it emphasizes effort/complexity instead of duration.
You don t need to know how long each task necessary to implement a backlog item in a sprint will take. What you need to know is, given the work you ve previously committed to in this sprint, can you commit to this backlog item? Because we know that we can t know exactly how much time each backlog item will take, we have to make an educated guess.
More important, what does it mean to fail in Scrum? Is not getting every sprint backlog item completed a failure? No... if you got four out of five items done and the fifth one is mostly done, you ll get credit for the four completed items (in terms of velocity for the sprint), and when you finish the remaining tasks for that fifth item in a future sprint you will get full credit for that item. But, would you have gotten any more done if you weren t using Scrum? The only failure in Scrum is failing to learn from your mistakes, to keep doing the same dysfunctional things repeatedly while expecting different results.
So, in your sprint planning meeting, don t spend a lot of time worrying about something you re not going to be able to know. Let the team think about the work, and then let them sign up for the amount of work they feel comfortable they can complete during the sprint. If they undercommit you can always drag something into the backlog, or end the sprint early. If they overcommit, then you finish the backlog items you can in priority order and discuss why the unfinished items couldn t be finished in the sprint retrospective, along with how to prevent having unfinished items in future sprints.
By the way, I know this was probably a poor choice of words on your part, but an effective Scrum Master doesn t run the sprint. The team runs the sprint, and the Scrum Master actively looks for impediments that lower their productivity and interfere with their ability to meet their commitments. Scrum Masters aren t managers, they re a combination of referee, coach, and scorekeeper. They are the Keeper of the Process, they help the team follow the process, they protect the team from outside agents that try to go around the process, and they track progress during the sprint via ensuring the sprint backlog is updated and the sprint burndown chart reflects reality, on a daily basis. In the situation you ve described, where the team isn t sure how much work they should sign up for, the Scrum Master should let the team decide as a reflection of respect for team ownership of the commitment. Whatever the decision is, it won t be wrong.