Question

Suppose Riley is interested in the cost of a gallon of gas in her state. She finds the cost of a gallon of regular gas at 61 randomly selected gas stations and calculates the mean price of gas to be $2.62. The standard error of the mean is $0.05. What is the standard deviation of the sample ( ???? )? Please round your answer to two decimal places.

Answer 1

Answer:

The standard deviation of the sample is 0.0064.

Step-by-step explanation:

The standard deviation of a sample of length n of a population with standard deviation $\sigma$ is given by the following formula:

$s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

61 randomly selected gas stations. This means that $n = 61$

The standard error of the mean is $0.05. This means that $\sigma = 0.05$.

What is the standard deviation of the sample?

$s = \frac{\sigma}{\sqrt{n}} = \frac{0.05}{\sqrt{61}} = 0.0064$

The standard deviation of the sample is 0.0064.