These practice problems focus on distinguishing discrete versus continuous random variables. Random variables represent quantities or qualities that randomly change within a population. Solve the following problems about discrete and continuous random variables.

## Sample questions

Which of the following random variables is discrete?

(A) the length of time a battery lasts

(B) the weight of an adult

(C) the percentage of children in a population who have been vaccinated against measles

(D) the number of books purchased by a student in a year

(E) the distance between a pair of cities

**Answer: D.**the number of books purchased by a student in a yearA discrete random variable is one that can take on only values that are integers (positive and negative whole numbers and 0). The values of a discrete random variable can have a finite stopping point, like –1, 0, and 1, or they can go to infinity (for example, 1, 2, 3, 4, . . . ).

A continuous random variable takes on all possible values within an interval on the real number line (such as all real numbers between –2 and 2, written as [–2, 2]).

A number of books takes on only positive integer values, such as 0, 1, or 2, and thus is a discrete random variable.

Which of the following random variables isn't discrete?

(A) the number of children in a family

(B) the annual rainfall in a city

(C) the attendance at a football game

(D) the number of patients treated at an emergency room in a day

(E) the number of classes taken in one semester by a student

**Answer: B.**the annual rainfall in a cityA discrete random variable is one that can take on only values that are integers (positive and negative whole numbers and 0). The values of a discrete random variable can have a finite stopping point, like –1, 0, and 1, or they can go to infinity (for example, 1, 2, 3, 4, . . . ).

A continuous random variable takes on all possible values within an interval on the real number line (such as all real numbers between –2 and 2, written as [–2, 2]).

The amount of rain that falls on a city in a year can take on any non-negative value on the real number line, such as 11.45 inches or 37.9 inches, and therefore is continuous rather than discrete.

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