Question

Decide whether the following statement represents a discrete random variable or a continuous random variable. distance a baseball travels after being hit

A) Discrete random variable.
B) Continuous random variable.

Answer 1

The distance a baseball travels after being hit is a continuous random variable because the distance is measured and can take on any value within a range, not just discrete increments.

Step-by-step explanation:

The distance a baseball travels after being hit would represent a continuous random variable. This is because the distance can be any value within a range and is not restricted to countable increments. Just as temperature and height are measured in degrees and inches respectively, the distance of a baseball is measured in feet or meters, depending on the unit of measurement used. These measurements can have fractional parts and are not merely counted but measured to determine the value.

To provide a further understanding using mathematical definitions:

a. Define the random variable. X = the distance a baseball travels after being hit

b. X~ (the representation of the distribution of the random variable X for continuous data)

c. Graph the probability distribution. (This would be a curve representing the continuous data)

d. The distribution is continuous.

Answer 2

The distance a baseball travels after being hit is a continuous random variable because its outcome is measured and can take on an infinite number of possible values within a certain range.

Step-by-step explanation:

The distance a baseball travels after being hit is a continuous random variable. The outcome of this variable is not countable but rather measured, similar to examples such as temperature or the height of a student. Continuous random variables can take on an infinite number of possible values within a given range, which in this case, could be the range of possible distances a baseball might travel.

Continuous random variables are essential in fields such as sports analytics and physics where precise measurements are crucial.