Central Limit Theorem Quiz

Consider a population with $$\mu=50$$  and $$\sigma=5$$ is taken. Find the mean of the sampling distribution of the sample mean with a sample size of 30.

Consider a population with $$\mu=50$$  and $$\sigma=5$$ is taken. Find the standard deviation of the sampling distribution of the sample mean with a sample size of 30.

The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the mean of the sampling distribution of the sample mean of the residents’ ages.

The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the standard deviation of the sampling distribution of the sample mean of the residents’ ages.

What happens to the shape of a sampling distribution of sample means as n increases?

It is known that the mean of the population of unicorns equals 1000, and the standard deviation equals 25. In a group of 20 randomly selected unicorns, what is the standard deviation of the sampling distribution?