Question

Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) The time until a projectile returns to earth. (b) The number of times a transistor in a computer memory changes state in one operation. (c) The volume of gasoline that is lost to evaporation during the filling of a gas tank. (d) The outside diameter of a machined shaft.

Answer 1

The time until a projectile returns to earth, the volume of gasoline lost to evaporation, and the outside diameter of a machined shaft are continuous random variables. The number of times a transistor changes state is a discrete random variable.

Step-by-step explanation:

To decide whether a discrete or continuous random variable is the best model for each given variable, we should determine if the variable can be counted or needs to be measured.

1. The time until a projectile returns to earth. This is a continuous random variable since time is measured and can take on any value within a range.

2. The number of times a transistor in a computer memory changes state in one operation. This is a discrete random variable since we count the number of changes in state.

3. The volume of gasoline that is lost to evaporation during the filling of a gas tank. This is a continuous random variable because volume lost to evaporation is measured and can vary continuously.

4. The outside diameter of a machined shaft. This would be a continuous random variable as well, as diameters are measured with precision instruments and are not counted.

Answer 2

a) continuous random variable; b) discrete random variable; c) continuous random variable; d) continuous random variable

Step-by-step explanation:

In the case of a), b), and d), the variables are continuous random variables, because all of them are measured in a continuous scale. It means that between any two values of the scale, you can find infinite values. Height of something, time, length, are all continuous variables. For example, the outside diameters of a machined shaft could be 30 mm or 31mm, but also it could be 30.1, 30.2, 30.3 and so on. You could measure any value in the scale. The volume of gasoline also can take any value in a continuous scale. The time until a projectile returns to Earth probably needs to be measured very accurately, so again you can expect any value in the scale. When you’ re studying continuous variables the tool that you’ re using to measure it would be your limit to define how many values you can find between other two values.

The number of times a transistor in a computer memory changes state in one operation is a discrete random variable. It can only take finite values (0, 1, 2 and so on), so you can’ t find infinite values between two values. Discrete values always represent exact quantities that can be counted.