Peter is the owner of a hardware supply shop. He has hired you to check his machine's calibration prior to starting production on a large order. To check this, you set the machine to create 2.0 inch nails and manufacture a random sample of 200 nails. That sample of nails has an average length of 2.024 inches with a standard deviation of 0.205 inches. Does this sample provide convincing evidence that the machine is working properly or should it be shut down for repairs? Justify your reasoning mathematically