Get expert advice and community support on IDNLearn.com. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.
Sagot :
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]
### 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]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.
