To find the standard deviation of the sampling distribution (often called the standard error) for the average number of water bottles consumed by one person in a year, we use the formula:
\[ \text{Standard Error (SE)} = \frac{\sigma}{\sqrt{n}} \]
where \( \sigma \) is the standard deviation of the population, and \( n \) is the sample size.
Given:
- Population standard deviation, \( \sigma = 49 \)
- Sample size, \( n = 100 \)
Now we can calculate the standard error:
\[ \text{SE} = \frac{49}{\sqrt{100}} = \frac{49}{10} = 4.9 \]
Therefore, the standard deviation of the sampling population (standard error) is 4.9.