The population of pop cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of 0.16 ounces. Given this information, the sampling distribution of the sample mean, , for a random sample of 16 cans will also be normally distributed with a standard deviation equal to 0.04.

Question

The population of pop cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of 0.16 ounces. Given this information, the sampling distribution of the sample mean,  , for a random sample of 16 cans will also be normally distributed with a standard deviation equal to 0.04.

Quizplus · Accepted Answer

This is true. The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution would be 0.16 / √16 = 0.04.

The Population of Pop Cans Filled by a Particular Machine