Suppose you work a part-time job and earn \$15 per hour. Draw a scatter diagram that might represent the relation between your gross pay and hours worked. Is this a deterministic relation or a probabilistic relation?

Verified step by step guidance

1. Identify the two variables involved: the number of hours worked (independent variable, usually on the x-axis) and the gross pay (dependent variable, usually on the y-axis).
2. Since you earn \$15 per hour, the gross pay can be calculated by the formula: \(\text{Gross Pay} = 15 \times \text{Hours Worked}\).
3. To draw the scatter diagram, plot points where the x-coordinate is the number of hours worked and the y-coordinate is the corresponding gross pay calculated using the formula above. For example, if you worked 1 hour, plot the point (1, 15); if you worked 2 hours, plot (2, 30), and so on.
4. Because the gross pay is exactly determined by the number of hours worked with no randomness, the points will lie perfectly on a straight line with slope 15 passing through the origin (0,0).
5. Conclude that this is a deterministic relation because the gross pay is completely determined by the hours worked without any variability or randomness.

Key Concepts

Scatter Diagram

A scatter diagram is a graphical representation that shows the relationship between two quantitative variables by plotting data points on a coordinate plane. Each point represents an observation with values for both variables, helping to visualize patterns, trends, or correlations.

Deterministic Relation

A deterministic relation means that one variable is exactly determined by another without any randomness. In this context, if gross pay is always calculated as hours worked multiplied by a fixed rate, the relationship is deterministic and predictable.

Probabilistic Relation

A probabilistic relation involves some randomness or uncertainty, where the outcome variable is not perfectly predictable from the input variable. If factors like bonuses or unpaid breaks affect gross pay, the relation between hours worked and pay would be probabilistic.