Question

Consider this random sample of data.

5, 33, 25, 55, 96, 75, 23, 69, 37, 17, 12

What is the sample proportion greater than the number 20?

A.
40.6%
B.
50%
C.
29.2%
D.
72.7%

Answer 1

To find the sample proportion greater than 20 in the given data set, we first need to count how many numbers in the sample are greater than 20.

The sample data is:
5, 33, 25, 55, 96, 75, 23, 69, 37, 17, 12

Now, let's count how many values are greater than 20:

- 33 > 20
- 25 > 20
- 55 > 20
- 96 > 20
- 75 > 20
- 23 > 20
- 69 > 20
- 37 > 20

The numbers greater than 20 are: 33, 25, 55, 96, 75, 23, 69, and 37. This gives us a total of 8 numbers.

The total number of observations in the sample is 11.

Now, we can calculate the sample proportion greater than 20:

\[
\text{Sample Proportion} = \frac{\text{Number of values greater than 20}}{\text{Total number of values}} = \frac{8}{11}
\]

To find this as a percentage:

\[
\frac{8}{11} \approx 0.7272
\]

Now, converting to percentage:

\[
0.7272 \times 100 \approx 72.72\%
\]

Rounding this gives us approximately \( 72.7\%\).

Thus, the correct answer is:

**D. 72.7%**