Standard deviation of sample mean

[ychych00]

Suppose we have a large population of houses in a community. The average annual heating expense for each house is $400 with a population standard deviation of $25. A random sample of 25 houses had a sample mean of $380 and a sample standard deviation of $35.

1.What is the mean of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses?

2.What is the standard deviation of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses?

3. Is it safe to assume that the sampling distribution of the sample mean for samples of size 25 is normally distributed? Why or why not?


Please help coz I have no idea...

 

[LightHero]

1. The mean of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses is $400.2. The standard deviation of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses is $25/√25 = $5.3. Yes, it is safe to assume that the sampling distribution of the sample mean for samples of size 25 is normally distributed. This is because according to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large (in this case, 25 is considered sufficiently large).