Determine whether the situation calls for a discrete or continuous random variable.
The braking time of a car
Is it discrete?
yes
To determine whether the situation calls for a discrete or continuous random variable, we need to understand the nature of the variable in question.
In this case, the braking time of a car refers to the time it takes for a car (or any vehicle) to come to a complete stop after the brakes are applied.
Now, let's consider the characteristics of a discrete random variable:
1. A discrete random variable can only take on specific values or outcomes.
2. There are gaps between the possible values of a discrete random variable.
On the other hand, a continuous random variable has the following characteristics:
1. A continuous random variable can take on any value within a specific range or interval.
2. There are no gaps or jumps between the possible values of a continuous random variable.
In the context of the braking time of a car, it is more appropriate to model it as a continuous random variable. This is because the time it takes for a car to brake can theoretically take on any value within a specific range, such as 2.3 seconds, 3.72 seconds, and so on. There is no restriction on the possible values, and there are no gaps or jumps between different braking times.
Therefore, the situation of braking time of a car calls for a continuous random variable.