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\begin{tabular}{|c|c|}
\hline
Semester & \begin{tabular}{c}
Student Applications \\
(in thousands)
\end{tabular} \\
\hline
1 & 106 \\
\hline
2 & 137 \\
\hline
3 & 285 \\
\hline
4 & 120 \\
\hline
5 & 202 \\
\hline
6 & 195 \\
\hline
7 & 327 \\
\hline
8 & 139 \\
\hline
10 & 307 \\
\hline
12 & 218 \\
\hline
\end{tabular}

The table shows the total number of student applications to universities in a particular state over a period of 12 semesters. Suppose the state decides that if fewer than 200,000 students apply during 6 or more semesters, they will make a special effort to promote university education. Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?

Sagot :

GinnyAnsweridn
To determine the population proportion of semesters for which the number of student applications is less than 200,000, we can follow these steps:

1. Identify the Data:
- The table lists the number of student applications (in thousands) for 12 semesters.
- Applications for each semester (in thousands) are: 106, 137, 285, 120, 202, 195, 327, 139, 307, 218.

2. Define the Threshold:
- The threshold is 200,000 students, which can be expressed as 200 (in thousands).

3. Count Semesters Below the Threshold:
- We need to count the number of semesters in which the number of applications was less than 200 (in thousands):
- Semester 1: 106 < 200 (below threshold)
- Semester 2: 137 < 200 (below threshold)
- Semester 3: 285 > 200 (not below threshold)
- Semester 4: 120 < 200 (below threshold)
- Semester 5: 202 > 200 (not below threshold)
- Semester 6: 195 < 200 (below threshold)
- Semester 7: 327 > 200 (not below threshold)
- Semester 8: 139 < 200 (below threshold)
- Semester 10: 307 > 200 (not below threshold)
- Semester 12: 218 > 200 (not below threshold)

- Therefore, the semesters with applications below the threshold are semesters 1, 2, 4, 6, and 8.

4. Number of Semesters Below Threshold:
- The total number of semesters below the threshold is 5.

5. Total Number of Semesters:
- The data comprises 10 semesters.

6. Calculate the Population Proportion:
- The population proportion is the ratio of the number of semesters below the threshold to the total number of semesters.
- Population proportion = Number of semesters below threshold / Total number of semesters
- Population proportion = 5 / 10
- Population proportion = 0.5

Therefore, the population proportion of semesters for which the number of student applications is less than 200,000 is 0.5, or 50%.
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