Which of the following is NOT a discrete random variable?
A. Number of refrigerator sell each day
B. Height of dragon fruit as measured each day
C. Number of students late in going to school each day
D. Number of people went to the doctor from Monday to Friday
The correct answer and explanation is :
The correct answer is B. Height of dragon fruit as measured each day.
Explanation:
To understand why option B is the correct answer, let’s first define what a discrete random variable is. A discrete random variable is one that takes on countable values. These values are distinct and separate, and they typically involve counting occurrences of some event or characteristic.
Let’s go over each option:
A. Number of refrigerators sold each day
This is a discrete random variable because it represents the count of refrigerators sold, which can only take whole number values (0, 1, 2, 3, etc.). You cannot sell a fraction of a refrigerator in this context, making it countable and discrete.
B. Height of dragon fruit as measured each day
Height is a continuous random variable, not discrete. Continuous random variables can take any value within a given range, including fractions or decimals. The height of a dragon fruit could be 10.1 cm, 10.01 cm, or even 10.001 cm, and there’s no restriction on the possible values it can take. Hence, it is not a discrete random variable.
C. Number of students late in going to school each day
This is a discrete random variable because the number of students late can only be counted as whole numbers (e.g., 0, 1, 2, etc.). It’s countable and distinct, making it discrete.
D. Number of people who went to the doctor from Monday to Friday
Similar to the other count-based options, this is a discrete random variable. The number of people who visited the doctor can only be a non-negative integer (e.g., 0, 1, 2, etc.), which makes it discrete.
Conclusion:
The key difference between discrete and continuous random variables lies in whether the variable is countable (discrete) or can take any value within a range (continuous). The height of a dragon fruit is continuous because it can take on an infinite number of possible values, whereas the other variables in the options are countable and distinct, thus making them discrete.