The population of Pepsi cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of.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 .04.

Question

The population of Pepsi cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of.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 .04.

Quizplus · Accepted Answer

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 population standard deviation is 0.16 and the sample size is 16, so the standard deviation of the sampling distribution is 0.16/sqrt(16) = 0.04. Therefore, the sampling distribution of the sample mean is also normally distributed with a standard deviation of 0.04.

The Population of Pepsi Cans Filled by a Particular Machine