Which of the following variable is discrete random variable?
A. The amount of unleaded gasoline in a Suzuki car
B. The temperature of a cup of coffee served at a restaurant.
C. The number of boys in a randomly selected three-child family
D. The average amount spent on water bill every month of December by a randomly selected household in Quezon Province.
The correct answer and explanation is :
The correct answer is C. The number of boys in a randomly selected three-child family.
Explanation:
A discrete random variable is a variable that can take on a countable number of distinct values, often involving whole numbers. These variables are typically the result of counting something, where each possible value corresponds to a distinct count.
Let’s break down each option:
- A. The amount of unleaded gasoline in a Suzuki car: This variable is continuous, not discrete. Gasoline can be measured in infinitely small units (e.g., liters, milliliters), and there is no limit to the precision with which it can be measured. As such, it is a continuous random variable because it can take any value within a given range, not just specific, countable values.
- B. The temperature of a cup of coffee served at a restaurant: Temperature is also a continuous random variable. It can take any value within a range and can be measured with great precision (e.g., 75.4°C, 75.45°C, 75.445°C). Like the gasoline example, temperature is not countable and can take on an infinite number of values within a certain range, making it a continuous variable.
- C. The number of boys in a randomly selected three-child family: This is a discrete random variable. It represents a count of the number of boys in a family, and this count can only take specific values: 0, 1, 2, or 3. You cannot have 1.5 boys, for example. The number of boys is countable, making it discrete.
- D. The average amount spent on a water bill every month of December by a randomly selected household in Quezon Province: This variable is continuous as well. Although it involves a monthly expense, the amount spent on a water bill is measurable and can vary continuously. It is not limited to discrete values and can take on any value within a range (e.g., 500 pesos, 500.5 pesos, 500.55 pesos, etc.), making it a continuous random variable.
Conclusion:
The number of boys in a three-child family is the only discrete variable among the options, as it involves a countable, finite set of possibilities (0, 1, 2, or 3). Therefore, C is the correct answer.