A continuous random variable is a random variable that has only continuous values. Continuous values are uncountable and are related to real numbers.  

Examples of continuous random variables:

1. Number of clients in a restaurant in one hour, 

2. Height of a person, 

3. Quantity of liquid in a bottle, 

For example, it would make no sense to find the probability it took exactly 30 minutes to finish an inspection. It might take you 30.31 minutes. The probability of points no longer makes sense from discrete to continuous random variables. Using the previous examples to illustrate this point:

1. Probability of having between ten to twenty clients in one hour [10, 20] clients.

2. Probability of randomly choosing a person whose height lies in the interval [1.70, 1.80] meters.

3. The volume of liquid in a bottle is between [0.5, 1.5] liters.

The main difference between continuous and discrete random variables is that continuous probability is measured over intervals, while discrete probability is calculated on exact points.

Instead, it is possible to find the probability of taking at least 30 minutes for an inspection or the probability of taking between 28 and 32 minutes to complete the inspection. Instead of assigning a probability to points, a probability density function (pdf) will be always related to a certain range of values. Probability can then be determined by finding the area under the function. But, to be a valid probability density function, the total area under the curve must equal 1.