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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 \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.

Sagot :

GinnyAnswer
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.
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