Can I design a survey with Jotform?

Yes, it's possible, I would recommend you to take a look on these survey templates: https://www.jotform.com/form-templates/category/survey 

You may find an existing form that meets your requirements and simply use it, this guide will help you suing form templates:  https://www.jotform.com/help/106-How-to-Use-Form-Templates 

Here is also an specific guide about how to create a survey form: https://www.jotform.com/help/158-How-to-create-a-survey-form-and-customize-it 

I hope this helps.