The population of soft drink cans filled by a particular machine is known to be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .25 ounce. Given this information, the sampling distribution for a random sample of n = 25 cans will also be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .05 ounce.

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be normally distributed if the population from which the sample is drawn is normally distributed. The mean of the sampling distribution ($\mu_{\bar{x}}$) is equal to the population mean ($\mu$), which is 12 ounces in this case. The standard deviation of the sampling distribution ($\sigma_{\bar{x}}$) is equal to the population standard deviation ($\sigma$) divided by the square root of the sample size ($n$), which calculates to $0.25 / \sqrt{25} = 0.25 / 5 = 0.05$ ounce.

The Population of Soft Drink Cans Filled by a Particular