A random variable is used to find the number of items in a scavenger hunt being held by a local youth group. Identify the variable is discrete or continuous and explain.
The variable in this case is the number of items in a scavenger hunt.
If the variable can only take on whole number values (such as 0, 1, 2, 3, etc.), then it is a discrete random variable. This would be the case if the scavenger hunt has a specific set of items that the participants need to find and there are no fractional or decimal quantities involved. For example, if the scavenger hunt involves finding specific objects like "find 6 apples" or "find 3 blue balloons", then the number of items is discrete.
On the other hand, if the variable can take on any real number value within a certain range (including fractional or decimal values), then it is a continuous random variable. This would be the case if the participants are not limited to finding specific items but can find any objects of their choice, and the number of items they find can be any non-negative real number. For example, if the participants can find any items they want and a participant could find 4.5 items or 7.2 items, then the number of items is continuous.