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\begin{tabular}{|c|c|c|c|c|}
\hline
Week & Job sat. score & Absence rate & Quality score & Output score \\
\hline
1 & 3.90 & 0.06 & 0.92 & 9 \\
\hline
2 & 3.80 & 0.05 & 0.91 & 11 \\
\hline
3 & 3.80 & 0.07 & 0.89 & 9 \\
\hline
4 & 3.90 & 0.04 & 0.84 & 8 \\
\hline
5 & 4.00 & 0.03 & 0.82 & 11 \\
\hline
6 & 4.10 & 0.03 & 0.92 & 9 \\
\hline
7 & 3.70 & 0.05 & 0.90 & 10 \\
\hline
8 & 4.40 & 0.06 & 0.82 & \\
\hline
\end{tabular}

Weekly goals:
- Job satisfaction score [tex]$\geq 4.40$[/tex]
- Absence rate [tex]$\leq 0.06$[/tex]
- Quality score [tex]$\geq 0.97$[/tex]
- Output score [tex]$\geq 11$[/tex]

Over the last four weeks, how is the team doing compared to the quality goal?

A. About [tex]$15\%$[/tex] below target
B. About [tex]$12\%$[/tex] below target
C. About [tex]$11\%$[/tex] below target


Sagot :

Let's solve this problem step-by-step:

1. Identify Relevant Weeks: This problem asks us to evaluate the quality score over the last four weeks. Let's identify these weeks and their corresponding quality scores from the given table:
- Week 5: Quality score = 0.82
- Week 6: Quality score = 0.92
- Week 7: Quality score = 0.90
- Week 8: Quality score = 0.82

2. Calculate the Average Quality Score: To determine how the team is performing, we first need to find the average quality score over these four weeks. The quality scores for the last four weeks are [tex]\(0.82, 0.92, 0.90, 0.82\)[/tex].

The average quality score can be calculated as:
[tex]\[ \text{Average Quality Score} = \frac{0.82 + 0.92 + 0.90 + 0.82}{4} = \frac{3.46}{4} = 0.865 \][/tex]

3. Determine the Target Quality Score: The target quality score given in the problem statement is 0.97.

4. Calculate the Percentage Below the Target: We need to calculate by what percentage the average quality score is below the target quality score. This can be done using the following formula:
[tex]\[ \text{Percentage Below Target} = \left(\frac{\text{Target Quality Score} - \text{Average Quality Score}}{\text{Target Quality Score}}\right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{Percentage Below Target} = \left(\frac{0.97 - 0.865}{0.97}\right) \times 100 \approx \left(\frac{0.105}{0.97}\right) \times 100 \approx 10.825 \% \][/tex]

Conclusion: The team's average quality score over the last four weeks is about [tex]\(0.865\)[/tex], which is approximately [tex]\(10.825\%\)[/tex] below the target quality score of [tex]\(0.97\)[/tex].

Thus, the correct option is:
- About [tex]\(11\% \)[/tex] below target.