Final answer:
The expected number of attendees at the dinner organized by a local arts council is denoted by variable X. This variable is used in probability and statistics to represent an uncertain quantity subject to change.
Step-by-step explanation:
The correct option that best represents the scenario of the local arts council organizing a dinner to thank supporters is a) The expected number of attendees at the dinner is denoted by X. This variable X typically signifies an unknown quantity that the council expects to attend, which may change until the actual event takes place, reflecting the uncertain nature of planning an event.
As for defining the random variable X in various contexts, it generally stands for a quantity that is random and susceptible to variation. For instance, X can represent the number of fencers who do not use the foil as their main weapon, the number of football players picked from a group of volunteers, or the number of students who do their homework on time.
Understanding how to define and use a random variable like X is crucial in probability and statistical analysis, which are important parts of Mathematics, especially when dealing with situations that involve uncertainty and variability.