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

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

Answer :

Sure, let's go through the steps to estimate how many high school students are expected to visit the store next week based on the given data.

1. Calculate Total Customers and Students Over the Given Weeks:
- In week 1: 2,848 customers and 2,033 students
- In week 2: 3,141 customers and 1,937 students
- In week 3: 3,861 customers and 2,076 students
- In week 4: 3,911 customers and 1,721 students

To find the total, sum up the numbers for all weeks:

- Total customers = 2,848 + 3,141 + 3,861 + 3,911 = 13,761
- Total students = 2,033 + 1,937 + 2,076 + 1,721 = 7,767

2. Calculate the Proportion of Students:

The proportion of students among the total customers is found by dividing the total number of students by the total number of customers:

- Proportion of students = Total students / Total customers = 7,767 / 13,761 ≈ 0.5644

3. Predict the Number of Students for Next Week:

Mary predicts there will be 4,238 customers next week. To find out how many of these might be high school students, multiply the predicted number of customers by the student proportion:

- Expected students next week = Predicted customers next week Proportion of students ≈ 4,238 0.5644 ≈ 2,392

Therefore, the store should expect approximately 2,392 high school students next week. The correct answer is b. 2,392.

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