Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

(a) The number of students in a randomly selected elementary school classroom.
(b) The amount of snow that falls in Minneapolis during the winter season.
(c) The flight time accumulated by a randomly selected Air Force fighter pilot.
(d) The number of points scored by the Miami Heat in a randomly selected basketball game.

A discrete variable is a variable whose value is obtained by counting and continuous variable is a variable whose value is obtained by measuring.
A random variable takes the value of integers and cannot be expressed in decimals where as a continuous variable takes all the value of an interval.

(a) The number of students in a randomly selected elementary school classroom.

Since the number of students are counted and can be never expressed in decimals that is 0.5 student does not make any sense. Thus, it is a discrete variable.

For example: 5 students, 8 students, 10 students

(b) The amount of snow that falls in Minneapolis during the winter season.

Since the length of snow fallen will be measured and can be expressed in decimal. it is a continuous variable.

For example: 15.8 inches of snow, 23 inches

(c) The flight time accumulated by a randomly selected Air Force fighter pilot.

Time is a continuous variable and can take any value between 0 and infinity. Thus, it is a continuous variable

For example: 4.6 seconds, 2.5 minutes, 8.5 hours

(d) The number of points scored by the Miami Heat in a randomly selected basketball game.

Since the number of points scored are counted and can be never expressed in decimals that is 0.5 points does not make any sense. Thus, it is a discrete variable.

For example: 32 points, 56 points, 12 points