Question

The average number of water bottles consumed by one person in a year is 156 with a standard deviation of 49. A survey of 100 people in your community was done to determine the probability that the average number of water bottles consumed per person per year is less than 150. In this scenario, what is the standard deviation of the sampling population?

Answer 1

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**.