Determine whether the value is a discrete random variable, continuous random variable, or not a random variable

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. The distance a baseball travels in the air after being hit. The exact time it takes to evaluate 27 + 72. The gender of college students. The amount of snowfall in December in a city. The weight of a one-pound steak. The square root of 9. Is the gender of college students a discrete random variable, continuous random variable, or not a random variable? Discrete random variable. Continuous random variable. It is not a random variable. Is the amount of snowfall in December a discrete random variable, continuous random variable, or not a random variable? Continuous random variable. Discrete random variable. It is not a random variable. Is the weight of a one-pound steak a discrete random variable, continuous random variable, or not a random variable? Random variable. Discrete random variable. It is not a random variable

The Correct Answer and Explanation is:

Here are the correct classifications for each situation, followed by a 300-word explanation:

1. The distance a baseball travels in the air after being hit – Continuous random variable
2. The exact time it takes to evaluate 27 + 72 – Continuous random variable
3. The gender of college students – It is not a random variable
4. The amount of snowfall in December in a city – Continuous random variable
5. The weight of a one-pound steak – Continuous random variable
6. The square root of 9 – It is not a random variable

Explanation

A random variable is a variable whose value is the result of a random process. It can be discrete (countable values like 0, 1, 2) or continuous (infinite possible values within an interval).

1. Distance a baseball travels: This can take any value depending on how hard it is hit, wind, and other factors. It can be 90.2 meters, 90.25 meters, and so on. Since it can have any value in a range, it is a continuous random variable.
2. Time to evaluate 27 + 72: While this may be very short, the exact time can differ per person or tool used and is measured with continuous units like seconds or milliseconds. It is a continuous random variable.
3. Gender of college students: Gender is a categorical variable. It is not numerical and cannot be measured in intervals or counted in the same way random variables are. Therefore, it is not a random variable.
4. Snowfall in December: Snowfall can be 5.2 cm, 12.75 cm, and so on. It is measurable and can vary continuously over an interval. This makes it a continuous random variable.
5. Weight of a one-pound steak: Even though labeled one pound, actual weight can vary slightly, like 1.02 or 0.98 pounds. It can take infinitely many values within a range, making it a continuous random variable.
6. Square root of 9: The square root of 9 is always exactly 3. It does not change or vary. Therefore, it is not a random variable.