Given a population mean of 27.1 with a standard deviation of 8.4 and a sample size of 10, answer these questions. part A: what is the standard deviation of the sampling distribution of x hat? show your work.
PartB: what does the sample size need to be if you want the standard deviation of the sampling distribution of x hat to be 2.8? show your work.

a) 2.66

b) 9

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

part A: what is the standard deviation of the sampling distribution of x hat? show your work.

We have that . So

PartB: what does the sample size need to be if you want the standard deviation of the sampling distribution of x hat to be 2.8?

This is n when . So

a is the right answer