Question

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

Short answer

The possible values of \(y\) (the depth of the lake at a randomly chosen point) range from 0 ft to 100 ft. And \(y\) is continuous, not discrete.

Step-by-step solution

Determining the range of the depth

As mentioned in the question, the lake has a maximum depth of 100 ft. It's also common knowledge that depth can't be a negative value. Therefore, the depth of the lake, \(y\), at any randomly chosen point can range anywhere from 0 ft (at the surface of the lake) to 100 ft (the maximum depth of the lake).

Determine the nature of the variable

The depth, \(y\), can take on any value within this range, not just distinct/separate values. For instance, it could be 17.5 ft, 43.2 ft, 60.9 ft etc. which are continuous fractions rather than discrete whole numbers. Therefore, \(y\) is a continuous variable, not discrete.