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The Correct Answer and Explanation is:
Question 1: Is the distance a baseball travels in the air after being hit a discrete random variable, a continuous random variable, or not a random variable?
Correct answer: B. It is a continuous random variable
Question 2: Is the number of fish caught during a fishing tournament a discrete random variable, a continuous random variable, or not a random variable?
Correct answer: A. It is a discrete random variable
Explanation (Around 300 words):
In statistics, a random variable is a variable whose possible values are numerical outcomes of a random phenomenon. Random variables are classified into two main types: discrete and continuous.
1. Distance a baseball travels:
The distance a baseball travels in the air after being hit is an example of a continuous random variable. This is because distance can take on any value within a range, including decimal values like 50.3 meters, 102.45 meters, or even 0.01 meters. You can measure the distance as precisely as the instrument allows. Since the exact distance is not known ahead of time and it depends on factors like the bat’s angle, wind speed, and force of the hit, it varies randomly and takes on infinitely many possible values within a range. Therefore, it is not discrete and not non-random.
2. Number of fish caught:
The number of fish caught during a fishing tournament is a discrete random variable. This is because the number of fish can only be whole numbers — for example, 0, 1, 2, 3, and so on. You cannot catch 2.5 fish. The value is counted, not measured. Since the number of fish caught varies based on chance (such as fishing skill, location, and luck), it is random and has a finite or countably infinite number of outcomes. Hence, it is classified as a discrete random variable.
In summary, distance is measured and continuous, while number of fish is counted and discrete. Both are random because they are determined by uncertain or unpredictable events.
