Question

A point is randomly selected on the surface of a lake that has a maximum depth of 100 feet. Let \(x\) be the depth of the lake at the randomly chosen point. What are possible values of \(x\) ? Is \(x\) discrete or continuous?

Short answer

Possible values of \(x\) are those in the interval \([0, 100]\). The variable \(x\) is continuous.

Step-by-step solution

Identify Possible Values of x

The possible values of \(x\) will be any depth from the surface of the lake to the maximum depth. Since the maximum depth is 100 feet, \(x\) can take any value between 0 (at the very surface) and 100 (the deepest point of the lake). Hence, the possible values for \(x\) are all real numbers in the interval \([0, 100]\).

Classify the Data Type

Considering that \(x\), the depth of the point chosen randomly on the lake, could assume at any real number value between 0 and 100, it is understood that \(x\) is a continuous variable. Discrete data can only take particular values whereas continuous data can take any value within a range. Here, the depth of the lake does not jump from one value to another, therefore \(x\) is continuous.