Is this normal or is my plant sick?
Yucca Plant Stalks Are All Spotted and Diseased Looking
Your yucca has apparently been infected with some type of fungal or bacterial disease. If it's a potted plant, you can try removing it from the pot, washing off all the old soil, and repotting in a clean container with fresh potting medium. If it's in the ground, you'll want to find out what the problem is if you want to save the plant. Here's an article about a common yucca disease: http://hyg.ipm.illinois.edu/pastpest/199912c.html
You can take leaf and soil samples to the nearest Extension Service for analysis. This link will help you locate an office: https://www.gardeningknowhow.com/extension-search/