To determine the expected number of understuffed chairs produced in a day, follow these steps:
1. Identify the proportion of understuffed chairs in the spot check:
The spot check revealed that there are 15 understuffed chairs out of a total of 300 chairs checked.
2. Calculate the proportion of understuffed chairs:
[tex]\[
\text{Proportion of understuffed chairs} = \frac{\text{Number of understuffed chairs}}{\text{Total number of chairs spot checked}} = \frac{15}{300}
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Proportion of understuffed chairs} = \frac{15}{300} = \frac{1}{20}
\][/tex]
3. Calculate the expected number of understuffed chairs per day:
The manufacturer produces 1500 chairs per day. Using the proportion calculated:
[tex]\[
\text{Expected number of understuffed chairs per day} = \text{Proportion of understuffed chairs} \times \text{Total chairs produced per day}
\][/tex]
Putting in the values:
[tex]\[
\text{Expected number of understuffed chairs per day} = \left(\frac{1}{20}\right) \times 1500
\][/tex]
4. Perform the multiplication:
[tex]\[
\left(\frac{1}{20}\right) \times 1500 = 75
\][/tex]
Therefore, the manufacturer would expect 75 chairs to be understuffed each day. The correct answer is:
They would expect 75 chairs to be understuffed.
