To determine how many understuffed chairs the manufacturer would expect to see in a production run of 1500 chairs per day, we can follow these steps:
1. Identify the proportion of understuffed chairs in the sample:
- From the sample data given, we see that there are 15 chairs that are understuffed out of a total of 300 chairs checked.
- To find the proportion of understuffed chairs, we use the formula:
[tex]\[
\text{Proportion of understuffed chairs} = \frac{\text{Number of understuffed chairs}}{\text{Total number of chairs in the sample}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Proportion of understuffed chairs} = \frac{15}{300} = 0.05
\][/tex]
2. Apply this proportion to the daily production volume:
- The manufacturer produces 1500 chairs per day.
- To estimate the number of understuffed chairs produced daily, we multiply the total daily production by the proportion of understuffed chairs:
[tex]\[
\text{Expected number of understuffed chairs per day} = \text{Proportion of understuffed chairs} \times \text{Total daily production}
\][/tex]
Substituting the given values:
[tex]\[
\text{Expected number of understuffed chairs per day} = 0.05 \times 1500 = 75
\][/tex]
So, they would expect 75 chairs to be understuffed in a production run of 1500 chairs per day.
Hence, the correct answer is:
- They would expect 75 chairs to be understuffed.
