johnson controller settings question

I have the digital model (a419) and I want the temp to be at 47 degrees. If I set the controller for 47, it seems like whenever i check it is about 10 degrees below what I set it at. Is this normally the case or is there another setting that i need to change on there to keep it closer to what I want all of the time? Another question I have is will the temp fluctuation be too much is if its colder like this?
This is my first time making a lager so I want to be sure I get it right. I made a 800 ml starter so I hope that is a start in the right direction. I am making an oktoberfest kit from northernbrewer

So, you're setting the temperature to 47F and the wort is 37F? Or, is the ambient air in the cooler (fridge?) 37F?

The first thing I would check is the temperature differential set in the controller. What is yours set to?

If you're missing your target temperature, I would recommend experimenting with alternative locations for the temperature probe. Experience has shown the best probe location to be on the outside of fermenter, insulated from ambient air temperature changes.

I dont have the wort in there yet, I am testing the controller before I brew today. It is the ambient air temp. The differential is set to 4. I will be somehow taping it to the side of the carboy when I put it in there today.

try it with a pail of water or something and tape it to the side and see if you get more reliable temps