I developed a quiz in Captivate and published it. But I can't save it in mp4 format to post to students.
You need to understand that MP4 video is not an interactive format suitable for a quiz.
If you sent a quiz question as a video, how would your users interact with it to choose the correct answer?
Welcome to the forum. Is my suspicion correct that you are new to Captivate and using the most recent version 12? At this moment two versions are supported simultaneously on one license;: version 12 and Captivate Classic. It helps to provide you with answers if you mention the version you are using. The full version number can be found under Help, about Captivate.
You don't 'save as' in Captivate: you have the raw Captivate file which you have edited, created the quiz. That project can be published to a format to enable it to distribute to your learners. The content of such a published format is not the same. Just one simple example: graphics will be compressed same as audio files (from WAV to MP3). The video format MP4 for publishing is only possible if you created a non-responsive project which is impossible with version 12. Hence the lack of publishing to MP4.
Moreover, as Rod points out, MP4 is a passive video format. Passive means that nothing can be changed while viewing the output. For a quiz you'll expect that the learner can answer questions and see the result, the score or even have that score registered in a Learning Management system. Interactivity is impossible in MP4 format. Play/pause video is not considered to be an interactivity.
How to provide the quiz to your learners? You will need to publish to HTML5. The result is like a website. You need to upload the output folder to a webserver and provide the learners with the URL pointing to the index.html file. Here is an example. I use part of my domain (lilybiri.com/published) as webserver:
Do not hesitate to ask more questions, but please mention the full version number.