Use the below code in Look & Feel->Style->Custom CSS.
#Questions{
background: lightskyblue;
}

https://www.qualtrics.com/community/discussion/comment/36058#Comment_36058Thanks for your responses. Your code did change the background colour of the questions. However, I hope to see each question shown in a separated block (as indicated in the above picture).

https://www.qualtrics.com/community/discussion/comment/36069#Comment_36069Slight update and this will add a whitespace between two questions.
#Questions .QuestionOuter {

background: lightskyblue;

}

What if we want to modify the background color of the response option instead?  Keep in mind there’s two colors.  One for when the page loads and one for when you mouse over the response option itself.

@dekennedy7 

How do I color-code my response options? | XM Community (qualtrics.com)

This thread should help, if you would like to change on hover and checked below css should work.

.Skin .MAVR label.MultipleAnswer, .Skin .SAVR label.SingleAnswer {

    background: #ffff;
}
.Skin label.MultipleAnswer.q-checked.q-focused,
.Skin label.SingleAnswer.q-checked.q-focused {
  background: #000;
}

.Skin label.MultipleAnswer.q-checked,
.Skin label.SingleAnswer.q-checked {
  background: #000;
}

.Skin .MAVR label.MultipleAnswer, .Skin .SAVR label.SingleAnswer {

    background: #ffff;
}
.Skin label.MultipleAnswer.q-checked.q-focused,
.Skin label.SingleAnswer.q-checked.q-focused {
  background: #000;
}

.Skin label.MultipleAnswer.q-checked,
.Skin label.SingleAnswer.q-checked {
  background: #000;
}

Thanks @Deepak!  Do I put this CSS into each individual question or the theme?  Or can I do either depending on whether I want to change the colors for a single question versus all questions?  Also, does it work on all question types?

@dekennedy7 

It works on Multiple/Single answer choice question type.

You can put it in Custom CSS within look and feel. 

If you want to do question specific you would need to include question ids in the same