Which of the following statement describe a continuous random variable?
a. The average distance traveled by a jeep in a week
b. The number of students present in a Class Anthurium
c. The number of motorcycle owned by a randomly selected household
d. The number of girls taller than 5 feet in a random sample of 10 girls
The correct answer and explanation is :
The correct answer is: a. The average distance traveled by a jeep in a week.
Detailed Explanation:
A continuous random variable is a variable that can take any value within a given range. It is not limited to isolated, separate numbers but instead can assume an infinite number of possible values within an interval. Examples include measurements like height, weight, time, and distance, where the value could be 5.1, 5.12, 5.123, and so on — infinitely precise.
Now, let’s analyze each choice carefully:
- a. The average distance traveled by a jeep in a week:
This is a continuous random variable because distance is a measurement. The distance traveled can be 100 miles, 100.5 miles, 100.567 miles, etc. There are no gaps between the possible values — it could be any value within a range depending on the situation. - b. The number of students present in a Class Anthurium:
This is a discrete random variable, not continuous. The number of students must be a whole number (e.g., 20, 21, 22 students). You cannot have 21.5 students present. Discrete variables count specific items or people. - c. The number of motorcycles owned by a randomly selected household:
Again, this is discrete. A household can own 0, 1, 2, 3 motorcycles — but not 2.7 motorcycles. It involves counting, which is characteristic of discrete random variables. - d. The number of girls taller than 5 feet in a random sample of 10 girls:
This is also discrete. We are counting how many girls meet a certain condition (being taller than 5 feet), and the count must be a whole number between 0 and 10.
Conclusion:
Among the options, only choice (a) describes a continuous random variable because distance can take on an infinite number of values within a certain range. The other options (b, c, and d) are all discrete random variables, because they involve counting specific, individual items without any fractional possibilities.