An inference
a. is a possible explanation for events using prior knowledge
b. explains if a hypothesis is or is not valid
c. is made independent of observation or prior knowledge
d. can be either qualitative or quantitative

The correct answer for the blank is -

a. is a possible explanation for events using prior knowledge.

Explanation:

An inference can be described as a conclusion or an opinion that is made or drawn on the basis of set of information or knowledge.

In other words, it is an explanation/conclusion for certain event (such as dance performance, singing, reciting poem) that is based on prior knowledge.

Thus, option a) is the right answer.