If the message you see is something like "you are missing a Spatial Reference", then the world file is alright. The world file cannot define the SR (spatial reference). To do this, right-click your image in Catalog, select Properties, scroll down to the Spatial Reference section, click "Edit" to define the Spatial Reference. This will generate a *.aux.xml file (for BMP) containing the SR information. Now, as you add the BMP image to ArcMap, you will not see the "missing SR" message.
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