Questions: Using this data, what is the sample proportion of semesters for which the number of student applications is less than 200,000 ? A. 42 % B. 33 % C. There is insufficient data to answer this question. D. 20 %

Solution Steps

To solve this problem, we need to determine the proportion of semesters where the number of student applications is less than 200,000. We will count the number of such semesters and then divide by the total number of semesters to get the sample proportion.

We need to count the number of semesters where the number of student applications is less than 200,000. Given the data:

\[ \text{applications} = [106, 137, 285, 120, 202, 195, 327, 139, 307, 318, 212, 217] \]

The semesters with applications less than 200,000 are:

\[ 106, 137, 120, 195, 139 \]

There are 5 such semesters.

The total number of semesters is:

\[ \text{total\_semesters} = 12 \]

The sample proportion of semesters with fewer than 200,000 applications is given by:

\[ \text{sample\_proportion} = \frac{\text{count\_below\_threshold}}{\text{total\_semesters}} = \frac{5}{12} \]

To express the sample proportion as a percentage:

\[ \text{sample\_proportion\_percentage} = \left( \frac{5}{12} \right) \times 100 \approx 41.67\% \]

Final Answer