Answered

Before a chair manufacturer sells its beanbag chairs, they spot-check a random sample of chairs on the production line. The table below shows the number of common problems found during one such spot-check.

\begin{tabular}{|c|c|}
\hline Common Problems & Frequency \\
\hline Open seam & 4 \\
\hline Cuts in upholstery & 14 \\
\hline Understuffed & 15 \\
\hline None & 267 \\
\hline Total & 300 \\
\hline
\end{tabular}

If the manufacturer makes 1500 beanbag chairs per day, how many of those chairs would they expect to be understuffed?

A. They would expect 15 chairs to be understuffed.
B. They would expect 75 chairs to be understuffed.
C. They would expect 300 chairs to be understuffed.
D. They would expect 750 chairs to be understuffed.



Answer :

GinnyAnswer
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.