How do you determine whether the quantitative variable is discrete or continuous given the length of a piece of string?

Hint: In order to give an answer to this question we need to recall the definition of continuous and discrete variable. Then according to the definition we get the answer if the quantitative variable is discrete or continuous for the given length of a piece of string.

Complete step by step solution:
We know that a discrete variable is a variable whose value is obtained by counting. A discrete random variable has a countable number of possible values. A random variable is a variable whose value is a numerical outcome. On the other hand a continuous variable is a variable whose value is obtained by measuring.
The length of a piece of a string has any value. So the length of a piece of string is a continuous variable.
Hence the quantitative variable is continuous for any given value of the length of a piece of string.

Note: Some examples of a discrete variable are number of glass marbles in a bag, number of blue marbles in an aquarium. Amount of sand particles in the desert is an example of a continuous variable. A variable holding any value between its maximum value and its minimum value then it is called a continuous variable otherwise it is called a discrete variable.