I'm in the Air Force, and I had the same thing at MEPS. The doctor handed me the paper and I read it aloud without even knowing why. Only after having read it with no issues, he told me it was to test for a stutter. Thankfully, I've never had as much of a problem reading stuff aloud. I also think not knowing about it/not dreading that moment and stressing about it, made a big difference. Since the cat is out of the bag now for OP, my best advice is just to not let it psych you out. You'll likely be tired and bored that day anyway, so try your best to put it to the back of your mind. Like you, I have a stammer and I'd consider it mild. Honestly the worst part about being in the military with a stammer was basic training. At least for the AF, whenever you talk to a MTI, you must start with a reporting statement ("Sir, trainee soandso reports as ordered"). If you're like many stutterers (and myself), I have difficulty saying my name, and manage to minimize my stammer by substituting difficult words. In this instance, and many others in the military, you can't avoid doing so. I was lucky to get a MTI who pulled me aside after my first difficulty with my reporting statement, and I explained my situation to him. Afterwards, he was very understanding and patient with me. After you graduate basic training, you should find things are alot more relaxed and not as stressful. Again, not trying to scare you. Just letting you know what you might be in for.