This situation with your 15-year-old is very concerning. We recommend that you immediately increase your monitoring of your son around the baby. Do not allow him to be around the baby without a responsible adult present. And when given a task, have him work where he can be continuously monitored.
Your son has shown that he cannot be trusted. Teach him that following instructions does include saying that he will follow them, but the next step is to begin the task immediately and to complete it to the best of his ability. The final step is to check back with the person who assigned the task.
If you are unsure how long it will take him to complete a task, ask him that question prior to giving the instruction. When the task is completed, compare what he told you to the actual time spent.
If you continue to have concerns, it may be helpful to schedule an appointment for him with a counselor. Sometimes as parents we try everything we can think of, but professional intervention is needed to make the necessary changes.