Classify the following as discrete or continuous random variables.


(A) The time it takes to run a marathon
(B) The number of fractions between 1 and 2
(C) A pair of dice is rolled, and the sum to appear on the dice is recorded
(D) The length of a broad jump

I got:
(A) Continuous
(B) Discrete
(C) Continuous
(D) Discrete
Is this correct?

A. Right

B. The fractions can get smaller and smaller.
C. Can you get 5 1/2 on the dice?
D. Can it be expressed in feet, inches and fractions of inches?

Your classifications are partially correct.

(A) The time it takes to run a marathon: Continuous
This is correct. The time it takes to run a marathon is a continuous random variable because it can take any value within a range (e.g., from 2 hours to 5 hours and beyond) with infinite possibilities.

(B) The number of fractions between 1 and 2: Discrete
This is incorrect. The number of fractions between 1 and 2 is also a continuous random variable since there are infinite possibilities between 1 and 2.

(C) A pair of dice is rolled, and the sum to appear on the dice is recorded: Discrete
This is correct. The sum of the numbers appearing on a pair of dice is a discrete random variable because there are a finite number of possible outcomes (2, 3, 4, ..., 11, or 12).

(D) The length of a broad jump: Continuous
This is correct. The length of a broad jump is a continuous random variable because it can take any value within a range (e.g., from 0 meters to several meters) with infinite possibilities.

So, the complete and correct classifications are:
(A) Continuous
(B) Continuous
(C) Discrete
(D) Continuous

Almost correct! Let's go through each random variable to verify the classification:

(A) The time it takes to run a marathon: This is a continuous random variable since it can take any non-negative value within a certain range, and there are infinite possible times.

(B) The number of fractions between 1 and 2: This is a discrete random variable since it can only take whole number values (1, 2, 3, ...). Fractions between 1 and 2 have a countable number of possibilities.

(C) The sum to appear on a pair of dice rolled: This is a discrete random variable since the sum can only take values from 2 to 12 (the numbers that can appear on two dice), and each of those values is a whole number.

(D) The length of a broad jump: This is a continuous random variable since the length can theoretically take any non-negative value within a certain range, including values in between (e.g., 10.5 feet). There are infinite possibilities for the length of a broad jump.

So the corrected classifications are:
(A) Continuous
(B) Discrete
(C) Discrete
(D) Continuous