Question

A random sample of size 16 is to be taken from a population that is normally distributed with a mean of 444 and a standard deviation of 32. The average of the observations in our sample is to be computed. What is the sampling distribution of the mean?

Answer 1

The sampling distribution of the mean can be approximated using the Central Limit Theorem. The mean of the sampling distribution of the mean will be equal to the population mean, and the standard deviation of the sampling distribution of the mean will be equal to the population standard deviation divided by the square root of the sample size.

Step-by-step explanation:

The sampling distribution of the mean can be approximated using the Central Limit Theorem. According to the Central Limit Theorem, if the sample size is sufficiently large, the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution. The mean of the sampling distribution of the mean will be equal to the population mean, and the standard deviation of the sampling distribution of the mean (also known as the standard error of the mean) will be equal to the population standard deviation divided by the square root of the sample size.