Question
A local government surveyed 200 households to estimate the annual spending on home utilities. The survey found that the average annual spending per household was $1,200, with a standard deviation of $100.
Estimate the total annual spending on home utilities for the entire community, assuming there are 8,500 households.
Select 1:
Question 1Answer
a.
$10,200,000
b.
$9,800,000
c.
$10,500,000
d.
$9,200,000
Question 2
Points 1
Question text
A survey company reports that 62% of people surveyed said that pepperoni was their favorite pizza topping, with a margin of error of ±5%
What range of pepperoni lovers percentage does this represent?
Select all that apply
Question 2Answer
a.
5%
b.
13%
c.
69%
d.
67%
e.
57%
Question 3
Points 1
Question text
A town hall surveyed 350 citizens to determine support for a new public transportation system. The survey showed that 38% of citizens supported the system, with a margin of error of 3%. If there are 4,800 citizens in the town, estimate how many citizens are likely to support the new transportation system.
Select 1:
Question 3Answer
a.
1,584 to 1,824
b.
1,680 to 1,872
c.
1,500 to 1,780
d.
1,700 to 1,940
Question 4
Points 1
Question text
To estimate the number of fish in a small lake, researchers caught 100 fish, tagged them, and returned them back to the lake.
The next day they caught 200 fish. Of those caught, 20 had a tag.
Estimate the amount of fish in the lake. Round your answer to the nearest whole number.
Question 4
Type answer here
Estimate the total annual spending on home utilities for the entire community, assuming there are 8,500 households.
Select 1:
Question 1Answer
a.
$10,200,000
b.
$9,800,000
c.
$10,500,000
d.
$9,200,000
Question 2
Points 1
Question text
A survey company reports that 62% of people surveyed said that pepperoni was their favorite pizza topping, with a margin of error of ±5%
What range of pepperoni lovers percentage does this represent?
Select all that apply
Question 2Answer
a.
5%
b.
13%
c.
69%
d.
67%
e.
57%
Question 3
Points 1
Question text
A town hall surveyed 350 citizens to determine support for a new public transportation system. The survey showed that 38% of citizens supported the system, with a margin of error of 3%. If there are 4,800 citizens in the town, estimate how many citizens are likely to support the new transportation system.
Select 1:
Question 3Answer
a.
1,584 to 1,824
b.
1,680 to 1,872
c.
1,500 to 1,780
d.
1,700 to 1,940
Question 4
Points 1
Question text
To estimate the number of fish in a small lake, researchers caught 100 fish, tagged them, and returned them back to the lake.
The next day they caught 200 fish. Of those caught, 20 had a tag.
Estimate the amount of fish in the lake. Round your answer to the nearest whole number.
Question 4
Type answer here
Answers
GPT-4o mini
Let's tackle each question one by one:
### Question 1:
**Estimate the total annual spending on home utilities for the entire community, assuming there are 8,500 households.**
To find the total spending, we multiply the average spending per household by the number of households:
\[
\text{Total Spending} = \text{Average Spending} \times \text{Number of Households} = 1,200 \times 8,500
\]
Calculating this:
\[
1,200 \times 8,500 = 10,200,000
\]
So, the answer is **a. $10,200,000**.
---
### Question 2:
**What range of pepperoni lovers percentage does this represent?**
The survey reports that 62% of people said pepperoni was their favorite topping, with a margin of error of ±5%. Therefore, we calculate the range:
- Lower limit: \(62\% - 5\% = 57\%\)
- Upper limit: \(62\% + 5\% = 67\%\)
Thus, the percentage range is from 57% to 67%. The options that apply are:
- **d. 67%**
- **e. 57%**
---
### Question 3:
**Estimate how many citizens are likely to support the new transportation system.**
The survey shows that 38% of citizens supported the system, with a margin of error of 3%. Thus, support ranges from:
- Lower limit: \(38\% - 3\% = 35\%\)
- Upper limit: \(38\% + 3\% = 41\%\)
Calculating the estimated number of supporters in the population of 4,800 citizens:
- Lower Estimate:
\[
0.35 \times 4800 = 1,680
\]
- Upper Estimate:
\[
0.41 \times 4800 = 1,968
\]
So the range of support is between 1,680 and 1,968. The closest option is:
**d. 1,700 to 1,940** (as this could represent a rounding or approximation).
---
### Question 4:
**Estimate the amount of fish in the lake.**
Using the capture-recapture method:
- Total fish caught first (tagged): \(100\)
- Total fish caught second (includes tagged): \(200\)
- Tagged fish recaptured: \(20\)
Using the formula for estimating wildlife populations:
\[
\text{Estimated Population} = \frac{\text{(Total tagged in first catch)} \times \text{(Total caught in second catch)}}{\text{(Tagged fish recaptured)}}
\]
Applying the numbers:
\[
\text{Estimated Population} = \frac{100 \times 200}{20} = 1000
\]
Thus, the estimated amount of fish in the lake is **1,000**.
---
Overall answers:
1. a. $10,200,000
2. d. 67%, e. 57%
3. d. 1,700 to 1,940
4. 1,000
### Question 1:
**Estimate the total annual spending on home utilities for the entire community, assuming there are 8,500 households.**
To find the total spending, we multiply the average spending per household by the number of households:
\[
\text{Total Spending} = \text{Average Spending} \times \text{Number of Households} = 1,200 \times 8,500
\]
Calculating this:
\[
1,200 \times 8,500 = 10,200,000
\]
So, the answer is **a. $10,200,000**.
---
### Question 2:
**What range of pepperoni lovers percentage does this represent?**
The survey reports that 62% of people said pepperoni was their favorite topping, with a margin of error of ±5%. Therefore, we calculate the range:
- Lower limit: \(62\% - 5\% = 57\%\)
- Upper limit: \(62\% + 5\% = 67\%\)
Thus, the percentage range is from 57% to 67%. The options that apply are:
- **d. 67%**
- **e. 57%**
---
### Question 3:
**Estimate how many citizens are likely to support the new transportation system.**
The survey shows that 38% of citizens supported the system, with a margin of error of 3%. Thus, support ranges from:
- Lower limit: \(38\% - 3\% = 35\%\)
- Upper limit: \(38\% + 3\% = 41\%\)
Calculating the estimated number of supporters in the population of 4,800 citizens:
- Lower Estimate:
\[
0.35 \times 4800 = 1,680
\]
- Upper Estimate:
\[
0.41 \times 4800 = 1,968
\]
So the range of support is between 1,680 and 1,968. The closest option is:
**d. 1,700 to 1,940** (as this could represent a rounding or approximation).
---
### Question 4:
**Estimate the amount of fish in the lake.**
Using the capture-recapture method:
- Total fish caught first (tagged): \(100\)
- Total fish caught second (includes tagged): \(200\)
- Tagged fish recaptured: \(20\)
Using the formula for estimating wildlife populations:
\[
\text{Estimated Population} = \frac{\text{(Total tagged in first catch)} \times \text{(Total caught in second catch)}}{\text{(Tagged fish recaptured)}}
\]
Applying the numbers:
\[
\text{Estimated Population} = \frac{100 \times 200}{20} = 1000
\]
Thus, the estimated amount of fish in the lake is **1,000**.
---
Overall answers:
1. a. $10,200,000
2. d. 67%, e. 57%
3. d. 1,700 to 1,940
4. 1,000