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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 of the 1500 beanbag chairs manufactured daily would be expected to be understuffed, we can follow these steps:

1. Determine the proportion of understuffed chairs in the random sample.
- From the table, we know that out of a total of 300 chairs, 15 are understuffed.
- The proportion of understuffed chairs in the sample is calculated as:
[tex]\[ \text{Proportion of understuffed chairs} = \frac{\text{Number of understuffed chairs}}{\text{Total number of chairs in sample}} = \frac{15}{300} = 0.05 \][/tex]

2. Calculate the expected number of understuffed chairs in the daily production.
- The manufacturer produces 1500 chairs per day.
- Using the proportion of understuffed chairs found in the sample, we can determine the expected number in the daily production by multiplying the production volume by the proportion:
[tex]\[ \text{Expected number of understuffed chairs} = \text{Daily production} \times \text{Proportion of understuffed chairs} = 1500 \times 0.05 = 75 \][/tex]

So, they would expect 75 chairs to be understuffed out of the 1500 chairs manufactured daily. Therefore, the correct answer is:

- They would expect 75 chairs to be understuffed.

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