Question

In a factory, each day the expected number of accidents is related to the number of overtime hour by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents. What is the expected number of accidents when no overtime hours are logged?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The Correct Option is B

To solve the problem, we'll derive the equation of the line that relates overtime hours to the expected number of accidents using the given points (1000, 8) and (400, 5). The equation of a line in slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 1: Calculate the slope \(m\).

The formula for the slope is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Substituting the given values:

\(m = \frac{5 - 8}{400 - 1000} = \frac{-3}{-600} = \frac{1}{200}\)

Step 2: Use the slope to find the y-intercept \(b\).

Substitute one of the points into the equation \(y = mx + b\). Let's use the point (1000, 8):

\(8 = \frac{1}{200} \cdot 1000 + b\)

\(8 = 5 + b\)

\(b = 3\)

Step 3: Write the equation of the line.

The equation is \(y = \frac{1}{200}x + 3\).

Step 4: Calculate the expected number of accidents when no overtime hours are logged, i.e., when \(x = 0\).

Substitute \(x = 0\) into the equation:

\(y = \frac{1}{200} \cdot 0 + 3 = 3\)

Conclusion: The expected number of accidents when no overtime hours are logged is 3.