Questions: 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 a region during the winter season (c) The flight time accumulated by a randomly selected military fighter pilot (d) The number of points scored by specific team in a randomly selected basketball game (a) Is the number of students discrete or continuous? A. The random variable is continuous. The possible values are x ≥ 0. B. The random variable is continuous. The possible values are x=0,1,2, ... C. The random variable is discrete. The possible values are x=0,1,2, ... D. The random variable is discrete. The possible values are x ≥ 0. (b) Is the amount of snow that falls discrete or continuous? A. The random variable is continuous. The possible values are x ≥ 0. B. The random variable is discrete. The possible values are x ≥ 0. C. The random variable is continuous. The possible values are x=0,1,2, ... D. The random variable is discrete. The possible values are x=0,1,2, ... (c) Is the flight time accumulated discrete or continuous? A. The random variable is discrete. The possible values are x=0,1,2, ... B. The random variable is continuous. The possible values are x ≥ 0. C. The random variable is continuous. The possible values are x=0,1,2, ... D. The random variable is discrete. The possible values are x ≥ 0.

Solution Steps

To determine whether a random variable is discrete or continuous, we need to understand the nature of the variable. A discrete random variable takes on a countable number of distinct values, while a continuous random variable takes on an infinite number of possible values within a given range.

(a) The number of students in a randomly selected elementary school classroom is a countable value, so it is a discrete random variable. The possible values are non-negative integers (0, 1, 2, ...).

(b) The amount of snow that falls in a region during the winter season can take on any value within a range, so it is a continuous random variable. The possible values are non-negative real numbers (x ≥ 0).

(c) The flight time accumulated by a randomly selected military fighter pilot can take on any value within a range, so it is a continuous random variable. The possible values are non-negative real numbers (x ≥ 0).

We need to classify each random variable as either discrete or continuous based on the nature of the values they can take.

1. Number of Students: This variable can take on values such as \(0, 1, 2, \ldots\), which are countable. Therefore, it is classified as a discrete random variable.
2. Amount of Snow: This variable can take on any non-negative real number, represented as \(x \geq 0\). Thus, it is classified as a continuous random variable.
3. Flight Time: Similar to the amount of snow, this variable can also take on any non-negative real number, represented as \(x \geq 0\). Hence, it is classified as a continuous random variable.

Next, we summarize the possible values for each random variable:

1. Number of Students: The possible values are \(0, 1, 2, \ldots\).
2. Amount of Snow: The possible values are \(x \geq 0\).
3. Flight Time: The possible values are \(x \geq 0\).

Final Answer