Question
You Try! A school district wants to estimate the total annual spending on school supplies by families in the district. They survey a random sample of 150 families and find that the average annual spending on school supplies in the sample is $620, with a standard deviation of $75.
Estimate the total annual spending on school supplies for the entire district, assuming there are 12,000 families.
Estimate the total annual spending on school supplies for the entire district, assuming there are 12,000 families.
Answers
GPT-4o mini
To estimate the total annual spending on school supplies for the entire district, we can use the average annual spending per family from the sample and multiply it by the total number of families in the district.
From the survey, here are the given values:
- Average annual spending per family (sample mean, \( \bar{x} \)) = $620
- Total number of families in the district = 12,000
Now, we can calculate the estimated total annual spending:
\[
\text{Total annual spending} = \text{Average annual spending per family} \times \text{Total number of families}
\]
Plugging in the values:
\[
\text{Total annual spending} = 620 \times 12,000
\]
Calculating this gives:
\[
\text{Total annual spending} = 7,440,000
\]
Therefore, the estimated total annual spending on school supplies by families in the district is **$7,440,000**.
From the survey, here are the given values:
- Average annual spending per family (sample mean, \( \bar{x} \)) = $620
- Total number of families in the district = 12,000
Now, we can calculate the estimated total annual spending:
\[
\text{Total annual spending} = \text{Average annual spending per family} \times \text{Total number of families}
\]
Plugging in the values:
\[
\text{Total annual spending} = 620 \times 12,000
\]
Calculating this gives:
\[
\text{Total annual spending} = 7,440,000
\]
Therefore, the estimated total annual spending on school supplies by families in the district is **$7,440,000**.