Answered

Select the correct answer.
Consider the following data set:
5, 33, 25, 55, 96, 75, 23, 69, 37, 17, 12.
A random sample of size 4 is drawn from the data set. It yields the following numbers: 5, 33, 17, and 23.
What is the population proportion greater than the number 20?
A.
33
B.
40.6
C.
29.2
OD.
50
E. 72.7

Verified Answer :

GinnyAnswer

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:
\(\[ \{5, 33, 25, 55, 96, 75, 23, 69, 37, 17, 12\} \]\)

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 \(\( p \)\) is calculated as:
\(\[ p = \left(\frac{\text{Number of elements greater than 20}}{\text{Total number of elements}}\right) \times 100 \]\)
Substituting the values:
\(\[ p = \left(\frac{8}{11}\right) \times 100 \]\)

5. Perform the calculation:
\(\[ \frac{8}{11} \approx 0.7273 \]\)
\(\[ 0.7273 \times 100 = 72.73 \]\)

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.

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