To solve the given problem, let's determine the population proportion of numbers greater than 20 in the data set.
1. Identify the data set:
[tex]\[
\{5, 33, 25, 55, 96, 75, 23, 69, 37, 17, 12\}
\][/tex]
2. Count the total number of elements in the data set:
The data set contains 11 elements.
3. Determine the number of elements greater than 20:
- The elements greater than 20 are: 33, 25, 55, 96, 75, 23, 69, 37
- Counting these elements, we have: 8 elements greater than 20
4. Calculate the population proportion of elements greater than 20:
Population proportion [tex]\( p \)[/tex] is calculated as:
[tex]\[
p = \left(\frac{\text{Number of elements greater than 20}}{\text{Total number of elements}}\right) \times 100
\][/tex]
Substituting the values:
[tex]\[
p = \left(\frac{8}{11}\right) \times 100
\][/tex]
5. Perform the calculation:
[tex]\[
\frac{8}{11} \approx 0.7273
\][/tex]
[tex]\[
0.7273 \times 100 = 72.73
\][/tex]
6. Compare the calculated proportion with the provided options:
The options are:
- A. 33
- B. 40.6
- C. 29.2
- D. 50
- E. 72.7
The calculated population proportion (72.73%) is closest to option E: 72.7.
Therefore, the correct answer is E. 72.7.
