Question

The owners of a large pet store have determined that \[65\%\] of their customers own dogs. They select \[15\] customers at random to survey. Let \[D\] be the number of customers they survey who have dogs. What type of variable is \[D\]?

Answer 1

The variable D is a discrete random variable as it counts the number of customers with dogs, with potential values ranging from 0 to 15.

Step-by-step explanation:

A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete.

In this scenario, the variable D represents the number of customers surveyed who own dogs, is a discrete random variable. This is because it arises from a counting process where the number of customers with dogs can only take on a finite or countable number of values.

The possible values that D can assume would range from 0 to 15, which are distinct and separate counts, as opposed to a continuous variable, which would take on any value within an interval on the number line.