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?(1 point) Responses 4.9 4.9 156 156 5.6 5.6 100

Answer 1

To find the standard deviation of the sampling population (often referred to as the standard error), you use the formula for the standard error of the mean (SEM), which is:

\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \]

where:

• \(\sigma\) is the population standard deviation
• \(n\) is the sample size

In this case:

• The population standard deviation (\(\sigma\)) is 49.
• The sample size (\(n\)) is 100.

Plugging in the numbers:

\[ \text{SEM} = \frac{49}{\sqrt{100}} = \frac{49}{10} = 4.9 \]

Therefore, the standard deviation of the sampling population is 4.9.