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In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store. She counted the number of customers who visited the store over the course of a month and found out how many of the customers were high school students. Her collected data is in the table below.

[tex]
\[
\begin{tabular}{|c|c|c|c|c|}
\hline
Week & 1 & 2 & 3 & 4 \\
\hline
Customers & 2,848 & 3,141 & 3,861 & 3,911 \\
\hline
Students & 2,033 & 1,937 & 2,076 & 1,721 \\
\hline
\end{tabular}
\]
[/tex]

Mary predicts that the store will see 4,238 customers next week. Approximately how many high school students should the store expect next week?

A. 1,865
B. 2,392
C. 2,446
D. 3,025

Please select the best answer from the choices provided.

Answer :

To solve this problem, we begin by estimating the percentage of customers who are high school students based on the data given for the month. Here are the steps:

1. First, we sum the number of customers over the four weeks:
[tex]$$
\text{Total Customers} = 2848 + 3141 + 3861 + 3911 = 13761.
$$[/tex]

2. Next, we sum the number of high school students over those weeks:
[tex]$$
\text{Total Students} = 2033 + 1937 + 2076 + 1721 = 7767.
$$[/tex]

3. The ratio of high school students to total customers is then:
[tex]$$
\text{Ratio} = \frac{7767}{13761} \approx 0.56442.
$$[/tex]

4. Mary predicts that there will be 4238 customers next week. To find the estimated number of high school students, we multiply the ratio by the predicted number of customers:
[tex]$$
\text{Predicted Students} = 4238 \times 0.56442 \approx 2392.02.
$$[/tex]

5. Since we are dealing with people, we round to the nearest whole number:
[tex]$$
\text{Predicted Students} \approx 2392.
$$[/tex]

Thus, the store should expect approximately 2392 high school students next week. The best answer among the provided choices is:

b. 2392

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