3
a worker randomly selects one out of every 7 sets from the 3,500 sets of headphones produced. the results are shown.
a. the population / sample is the total of 3,500 sets of headphones produced. the 500 selected for testing is the population / sample.
b. write the ratio of defective headphones to total headphones in the sample. then write the ratio as a decimal and as a percent.
\frac{4}{500}= = %
c. write and solve an equation to find the number of headphones in the population that can be estimated to be defective.
y = \frac{4}{500} \cdot 3,500
there would be about defective headphones.
check understanding
1. william conducted a random survey of the students in his school regarding the number of hours of sleep they got last night. the box plot shows the results of his survey. make an inference about the entire population.

2. hazel assigned a number to each of the 100 students in the band and put the numbers in a bag. she randomly chose 20 numbers and found that 3 students did not complete their homework for today. make an inference about the number of students in the band that did not do their homework. if hazel randomly chose 20 more numbers, what results would you expect? explain.

Question

3
a worker randomly selects one out of every 7 sets from the 3,500 sets of headphones produced. the results are shown.
a. the population / sample is the total of 3,500 sets of headphones produced. the 500 selected for testing is the population / sample.
b. write the ratio of defective headphones to total headphones in the sample. then write the ratio as a decimal and as a percent.
\frac{4}{500}=  =  %
c. write and solve an equation to find the number of headphones in the population that can be estimated to be defective.
y = \frac{4}{500} \cdot 3,500
there would be about  defective headphones.
check understanding
1. william conducted a random survey of the students in his school regarding the number of hours of sleep they got last night. the box plot shows the results of his survey. make an inference about the entire population.

2. hazel assigned a number to each of the 100 students in the band and put the numbers in a bag. she randomly chose 20 numbers and found that 3 students did not complete their homework for today. make an inference about the number of students in the band that did not do their homework. if hazel randomly chose 20 more numbers, what results would you expect? explain.

Accepted Answer

### Part A
# Brief Explanations:
- **Population**: The entire group we want to study, here all 3,500 headphones.
- **Sample**: A part of the population selected for testing, here 500 selected.
# Answer:
The population is the total of 3,500 sets of headphones produced. The 500 selected for testing is the sample.

### Part B
# Explanation:
## Step1: Find the ratio of defective to total in sample
The number of defective in sample is 4, total in sample is 500. So the ratio is $\frac{4}{500}$.
## Step2: Convert ratio to decimal
Divide 4 by 500: $4\div500 = 0.008$.
## Step3: Convert decimal to percent
Multiply decimal by 100: $0.008	imes100 = 0.8\%$.
# Answer:
$\frac{4}{500}=0.008 = 0.8\%$

### Part C
# Explanation:
## Step1: Identify the formula
The formula is $y=\frac{4}{500}\cdot3500$, where $\frac{4}{500}$ is the proportion of defective in sample, and 3500 is the population size.
## Step2: Solve the equation
First, simplify $\frac{4}{500}=\frac{1}{125}$. Then $y=\frac{1}{125}	imes3500$. Calculate $3500\div125 = 28$.
# Answer:
There would be about 28 defective headphones.

### Check Understanding 1
# Brief Explanations:
From the box - plot (assuming the box - plot has a median, quartiles etc. centered around a certain number of hours, say around 6 - 8 hours as per the axis). We can infer that most students in the school got a number of hours of sleep that is within the range shown in the box - plot. For example, if the box - plot shows that the middle 50% of students (the box) is between, say, 5 and 8 hours, we can infer that most students in the school got between 5 and 8 hours of sleep last night. (The exact inference depends on the box - plot details, but generally, we use the sample (survey) data to infer about the population (all students in the school)).
# Answer:
Most students in the school likely got a number of hours of sleep within the range shown by the box - plot (e.g., if the box is between 5 and 8 hours, most students got 5 - 8 hours of sleep last night).

### Check Understanding 2
# Brief Explanations:
- **Inference about total non - homework students**:
The proportion of non - homework students in the sample (20 students) is $\frac{3}{20}$. To find the estimated number in the population (100 students), we use the formula: Estimated number $=\frac{3}{20}	imes100 = 15$. So we can infer that about 15 students in the band did not do their homework.
- **Expectation for next sample**:
Since the sampling is random and we expect the proportion to be approximately the same (due to the law of large numbers, as we take more samples, the sample proportion should approach the population proportion), if we choose 20 more numbers, we would expect about $\frac{3}{20}	imes20 = 3$ students (or a number close to 3) who did not complete their homework, because the proportion of non - homework students in the population is expected to be stable, and the sample proportion should be a good estimate.
# Answer:
- Inference: About 15 students in the band did not do their homework.
- Expectation: If 20 more numbers are chosen, we would expect about 3 students (or a number close to 3) who did not complete their homework, as the sample proportion should be close to the population proportion.

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QUESTION IMAGE

Question

Explanation:

Part A

Step1: Find the ratio of defective to total in sample

Step2: Convert ratio to decimal

Step3: Convert decimal to percent

Step1: Identify the formula

Step2: Solve the equation

Answer:

Part B