Question

For each of the following, find the mean and standard deviation of the sampling distribution of the sample mean. State if the sampling distribution is normal, approximately normal, or unknown.

a. The population is skewed right with a mean of 4 and a standard deviation of 6. Many samples of size 100 are taken.

b. The population is normal with a mean of 61 and a standard deviation of 9. Many samples of size 900 are taken.

c. The population is skewed left with a mean of 15 and a standard deviation of 3. Many samples of size 25 are taken.

d. The population is normal with a mean of 73 and a standard deviation of 5. Many samples of size 16 are taken.

answer to all 4 please and thank you!

Answer 1

a. The population is skewed right with a mean of 4 and a standard deviation of 6. Many samples of size 100 are taken.

if the population is not normal but sample size taken is more than 30 then by central limit theorem the distribution tends to approximately normal

b. The population is normal with a mean of 61 and a standard deviation of 9. Many samples of size 900 are taken.

if the population is normal and sample size taken is more than 30 then by central limit theorem the distribution tends to normal

c. The population is skewed left with a mean of 15 and a standard deviation of 3. Many samples of size 25 are taken.

if the population is not normal and sample size taken is less than 30 then it is unknown

d. The population is normal with a mean of 73 and a standard deviation of 5. Many samples of size 16 are taken.

if the population is normal and sample size taken is less than 30 then by central limit theorem the distribution tends to approximately normal