Question

how are continuous random variables used in industry research, academic research, and scientific research.

Answer 1

The normal distribution is the most widely used probability distribution in world, which is a continuous distribution.

Continuous distribution: Every real number in the range has a probability.

Example of industrial use:

Surface roughness measurement of a component involves normal distribution. A component is accepted when it is very near to optimum roughness not more not less. Obtained roughness values, not integers they are continuous outcomes.

Example of academic research:

Percentage of performance of students in an institute is always continuous. It is having real values and for each real value, there is a probability of occurrence.

Example of scientific research:

The amount of radioactive uranium 235 needed to start a nuclear reaction. For every amount, there is a probability of nuclear reaction.