To solve this problem, we need to go through the random digits provided, interpret them according to the given rules, and compute the proportion of trials where more than 2 packages were selected before finding a package that was not delivered on time.
### Step-by-Step Solution
1. Extract Random Digits:
- We have a table of random digits given in a list format.
- We start from the beginning and treat each 2-digit number as a package outcome.
- The packages are inspected sequentially.
2. Interpret Digits:
- If a 2-digit number is between 00-04, it indicates a package not delivered on time.
- If a 2-digit number is between 05-99, it indicates a package delivered on time.
3. Perform 5 Trials:
- Continue examining numbers until a not-delivered-on-time package is found.
- Count how many packages were checked before finding the not-delivered-on-time package.
- Stop after 5 trials.
4. Determine Proportion:
- Count how many of these trials required checking more than 2 packages before finding the not-delivered-on-time package.
- Compute the proportion of such trials out of the total number of trials (5 trials).
### Execution
Here's the approach broken down by the random digits available.
- Random Digits:
```
"31640", "43402", "96003", "10498", "01532", "73869",
"67940", "85019", "98036", "98252", "43838", "45644",
"21805", "26727", "73239", "53929", "42564", "17080"
```
- 5 Trials Extraction & Counting:
- Trial 1: 31, 64, 04 -> Found `not delivered on time` at 3rd position (2 packages delivered before this one).
- Trial 2: 34, 02 -> Found `not delivered on time` at 2nd position (1 package delivered before this one).
- Trial 3: 96, 00 -> Found `not delivered on time` at 2nd position (1 package delivered before this one).
- Trial 4: 10, 49, 80, 15 -> Found `not delivered on time` at 4th position (3 packages delivered before this one).
- Trial 5: 32, 73, 86, 94, 08 -> Found `not delivered on time` at 5th position (4 packages delivered before this one).
### Analysis of Results
- Packages checked more than twice:
- Trial 1: Checked 2 packages before `not delivered`.
- Trial 4: Checked 3 packages before `not delivered`.
- Trial 5: Checked 4 packages before `not delivered`.
- Proportion Calculation:
- Out of the 5 trials, 3 trials needed more than 2 packages to be checked.
### Conclusion
The proportion can be calculated as:
[tex]\[ \text{Proportion} = \frac{\text{Number of trials with more than 2 selections}}{\text{Total number of trials}} = \frac{3}{5} = 0.6 \][/tex]
Thus, the shipping company can expect that more than 2 packages will need to be checked before finding one that was not delivered on time, 60% of the time.
The correct answer is:
[tex]\[ \boxed{0.6} \][/tex]
