The sample data that you have shared already has points created and it seems like at the same location. I just want to confirm that your data extent is the country boundary and the points should be placed within that extent.
If this is the case please try out the following:
1) Open Create Random Points tool.
2) Provide the output location where the point feature class or the shapefile will be created.
3) Name of the feature class or the shapefile.
4) Constraining Feature Class should be the country boundary.
5) Specify the total number of point features you want to create.
Let the other settings be default.
~Shan
~Shan