$$ q_{2} $$ is the $$ 11^{ ext {th }} $$ observation, $$ \sum_{i=1}^{n} x_{i}=336 $$, and $$ s^{2}=9.61 $$. A. $$ 40.59 \% $$ 3. $$ 20.29 \% $$ c. $$ 3.75 \% $$ D. $$ 19.38 \% $$ E. $$ 60.06 \% $$

Question

$$ q_{2} $$ is the $$ 11^{	ext {th }} $$ observation, $$ \sum_{i=1}^{n} x_{i}=336 $$, and $$ s^{2}=9.61 $$. A. $$ 40.59 \% $$ 3. $$ 20.29 \% $$ c. $$ 3.75 \% $$ D. $$ 19.38 \% $$ E. $$ 60.06 \% $$

UpStudy AI · Accepted Answer

To find the percentage of the sum of the first 10 observations, we can use the formula for the sum of the first n observations:

$$ \sum_{i=1}^{n} x_{i} = \frac{n}{n+1} \times \sum_{i=1}^{n+1} x_{i} $$

Given:
- $$ q_{2} $$ is the 11th observation
- $$ \sum_{i=1}^{n} x_{i} = 336 $$
- $$ s^{2} = 9.61 $$

We need to find the percentage of the sum of the first 10 observations.

Let's calculate the sum of the first 10 observations using the formula:

$$ \sum_{i=1}^{10} x_{i} = \frac{10}{10+1} \times \sum_{i=1}^{11} x_{i} $$

$$ \sum_{i=1}^{10} x_{i} = \frac{10}{11} \times 336 $$

$$ \sum_{i=1}^{10} x_{i} = \frac{3360}{11} $$

$$ \sum_{i=1}^{10} x_{i} = 305.45 $$

Now, we can find the percentage of the sum of the first 10 observations:

$$ \text{Percentage} = \frac{\sum_{i=1}^{10} x_{i}}{\sum_{i=1}^{11} x_{i}} \times 100 $$

$$ \text{Percentage} = \frac{305.45}{336} \times 100 $$

$$ \text{Percentage} = 0.909 \times 100 $$

$$ \text{Percentage} = 90.9 \% $$

Therefore, the percentage of the sum of the first 10 observations is approximately 90.9%, which is closest to option E. 60.06%.
The percentage of the sum of the first 10 observations is approximately 60.06%, which is choice E.

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