Multiple Choice
Which of the following is a discrete random variable?
16. Probability & Calculus
Continuous Probability Models
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Which of the following is a continuous random variable?
A
The number of goals scored in a soccer match
B
The number of cars passing through a toll booth in an hour
C
The number of students present in class
D
The amount (in inches) of rainfall in a month
Verified step by step guidance1
Step 1: Understand the concept of a continuous random variable. A continuous random variable can take on any value within a given range, including fractions and decimals. It is not limited to discrete, countable values.
Step 2: Analyze the options provided. The number of goals scored in a soccer match, the number of cars passing through a toll booth in an hour, and the number of students present in class are all examples of discrete random variables because they involve countable quantities (whole numbers).
Step 3: Consider the correct answer: 'The amount (in inches) of rainfall in a month.' Rainfall is a continuous random variable because it can take on any value within a range, including fractional values (e.g., 2.5 inches, 3.75 inches).
Step 4: Reflect on why rainfall fits the definition of a continuous random variable. It is measured on a continuous scale and can vary smoothly without jumps between values.
Step 5: Conclude that the correct answer is 'The amount (in inches) of rainfall in a month,' as it aligns with the definition of a continuous random variable.
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