The weight of bags of potato chips produced by one machine at a packaging plant has a standard deviation of 0.3 ounces. A sample of chip bags is to be drawn and the mean weight calculated. How large must the sample be if the standard deviation of the sampling distribution is to be 0.1 ounce?
A) 9 bags
B) 3 bags
C) 6 bags
D) 10 bags

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution (often called the standard error) is given by the formula $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. We are given $\sigma = 0.3$ ounces and want $\sigma_{\bar{x}} = 0.1$ ounce. Solving for $n$, we get $n = \left(\frac{0.3}{0.1}\right)^2 = 9$.

The Weight of Bags of Potato Chips Produced by One