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The cumulative distribution function takes data from the probability distribution function and adds up the probabilities for each successive event to give the probability that the event will be a certain value or less.

For example, say the manager of an office has a lot of work for people in his office to do and wants to know how many will call in sick on Friday. There are eight employees in the office.

Convert this to a cumulative probability distribution starting with \#2, then \#3, and so on.

\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 \\
Probabilities
\end{tabular} \\
\hline
1 & 0.10 & 0.10 \\
\hline
2 & 0.15 & 0.25 \\
\hline
3 & 0.20 & \\
\hline
4 & 0.20 & \\
\hline
5 & 0.14 & \\
\hline
6 & 0.10 & \\
\hline
7 & 0.07 & \\
\hline
8 & 0.04 & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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.

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