Question
The manager of a factory collected data in order to analyze the relationship between the number of hours of training a worker receives and the worker's error rate. The line of best fit for the collected data is y equals 0.1 minus 0.005 x, where x is the number of hours of training a worker receives and y is the error rate.
What approximate error rate should the manager expect for a worker who receives 6 hours of training?
Answer options with 4 options
A.
0.01
B.
0.07
C.
0.13
D.
0.17
What approximate error rate should the manager expect for a worker who receives 6 hours of training?
Answer options with 4 options
A.
0.01
B.
0.07
C.
0.13
D.
0.17
Answers
GPT-4o mini
To find the approximate error rate for a worker who receives 6 hours of training, we can substitute \( x = 6 \) into the equation of the line of best fit:
\[
y = 0.1 - 0.005x
\]
Substituting \( x = 6 \):
\[
y = 0.1 - 0.005(6)
\]
Calculating \( 0.005(6) \):
\[
0.005 \times 6 = 0.03
\]
Now substituting this back into the equation:
\[
y = 0.1 - 0.03
\]
\[
y = 0.07
\]
Therefore, the approximate error rate the manager should expect for a worker who receives 6 hours of training is **0.07**.
Thus, the correct answer is:
**B. 0.07**
\[
y = 0.1 - 0.005x
\]
Substituting \( x = 6 \):
\[
y = 0.1 - 0.005(6)
\]
Calculating \( 0.005(6) \):
\[
0.005 \times 6 = 0.03
\]
Now substituting this back into the equation:
\[
y = 0.1 - 0.03
\]
\[
y = 0.07
\]
Therefore, the approximate error rate the manager should expect for a worker who receives 6 hours of training is **0.07**.
Thus, the correct answer is:
**B. 0.07**