Final answer:
The height of a randomly selected giraffe is a continuous random variable because it is measured and can take on an infinite number of values within a range.
Step-by-step explanation:
The height of a randomly selected giraffe is an example of a continuous random variable. This is because height is measured rather than counted, and it can vary with infinitely fine gradations. Unlike discrete variables that are countable, like the number of books in a backpack, continuous variables are measured, like the height or weight of an object. Just as the temperature can be 68°, 71.5°, 80.6°, or 90.32°, a giraffe’s height can also range with similar precision. It is not restricted to whole-number increments, making it uncountable and continuous. For instance, a giraffe might be 14 feet, 3 and 5/8 inches tall, instead of simply 14 or 15 feet tall.
Understanding the difference between discrete and continuous variables is essential, as it affects how the data are analyzed statistically. With continuous data, you can calculate values like mean and standard deviation, which require intervals of data. In contrast, discrete data typically involve calculations of probabilities for distinct, separate values.
Since the height of a giraffe is a continuous variable, we could, for example, determine the probability of a giraffe being between 15 and 16 feet tall but not count how many giraffes are exactly 15 feet tall since the height measure includes an infinite number of possible values between any two heights.