Certainly! Let's complete the table step-by-step by calculating the cumulative probabilities for each successive employee.
### Step-by-Step Calculation:
1. Employee 1:
- Probability of calling in sick: 0.10
- Cumulative probability: 0.10 (since it's the first entry and there are no previous probabilities to add)
2. Employee 2:
- Probability of calling in sick: 0.15
- Cumulative probability: 0.10 (previous cumulative probability) + 0.15 = 0.25
3. Employee 3:
- Probability of calling in sick: 0.20
- Cumulative probability: 0.25 (previous cumulative probability) + 0.20 = 0.45
4. Employee 4:
- Probability of calling in sick: 0.20
- Cumulative probability: 0.45 (previous cumulative probability) + 0.20 = 0.65
5. Employee 5:
- Probability of calling in sick: 0.14
- Cumulative probability: 0.65 (previous cumulative probability) + 0.14 = 0.79
6. Employee 6:
- Probability of calling in sick: 0.10
- Cumulative probability: 0.79 (previous cumulative probability) + 0.10 = 0.89
7. Employee 7:
- Probability of calling in sick: 0.07
- Cumulative probability: 0.89 (previous cumulative probability) + 0.07 = 0.96
8. Employee 8:
- Probability of calling in sick: 0.04
- Cumulative probability: 0.96 (previous cumulative probability) + 0.04 = 1.00
### Filled Table:
\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{c}
Employee \\
[tex]$\#$[/tex]
\end{tabular} & \begin{tabular}{c}
Probability of \\
Calling in Sick
\end{tabular} & \begin{tabular}{c}
Cumulative \\
Probability
\end{tabular} \\
\hline 1 & 0.10 & 0.10 \\
\hline 2 & 0.15 & 0.25 \\
\hline 3 & 0.20 & 0.45 \\
\hline 4 & 0.20 & 0.65 \\
\hline 5 & 0.14 & 0.79 \\
\hline 6 & 0.10 & 0.89 \\
\hline 7 & 0.07 & 0.96 \\
\hline 8 & 0.04 & 1.00 \\
\hline
\end{tabular}
By filling out each step, you can see how the cumulative probabilities are built up from the individual probabilities.
