Suppose you tell one of your fellow students that when working with a continuous distribution, it does not make sense to try to compute the probability of any specific value since it will be zero. She says that, when the experiment is performed some value must occur, the probability can’t be zero. Your task is to respond to her statement and in doing so explain why it is appropriate to find the probability for specific ranges of values for a continuous distribution.
A continuous random variable may have any value in a specific range and because a certain value may have infinite numbers after the decimal, we should define the interval before calculating the probability. When random variables have continuous distribution, there is no point to calculate the probability at a single point. Meaning that we have to make sure the value falls within the interval.
Answer 2: Since you measure data only to a finite precision the result you report will already have a range instead of a specific value. This means that the probability that another measurement will give the same result is not zero. There is no point to measure an infinite precision. This is why it would make more sense to define the interval before trying to find the probability.