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)

Question

Responses

5.6
5.6

100
100

4.9
4.9

156

Answer 1

In this scenario, we want to find the standard deviation of the sampling distribution of the sample mean (the sampling population). We will use the formula for the standard error (SE) of the mean, which is given by:

\[ SE = \frac{\sigma}{\sqrt{n}} \]

where:

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

Here, \(\sigma = 49\) and \(n = 100\).

Now, let's calculate the standard error:

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

Therefore, the standard deviation of the sampling population (standard error) is 4.9.

The correct answer is 4.9.