A large set of numbers a population has an average of 200 an

A large set of numbers (a population) has an average of 200 and a standard deviation of 50.  

a)   If a sample a sample of 25 is taken form the population how close to 200 will the sample average tend to be?

b)   If a sample a sample of 100 is taken form the population how close to 200 will the sample average tend to be?

c)   If a sample a sample of 2500 is taken form the population how close to 200 will the sample average tend to be?

Solution

The average distance from the mean is the standard error of the means.

Thus:

a)

The standard error of the mean here is

sigma(Xbar) = sigma/sqrt(n)

= 50/sqrt(25)

= 10 [ANSWER]

*****************

b)

The standard error of the mean here is

sigma(Xbar) = sigma/sqrt(n)

= 50/sqrt(100)

= 5 [ANSWER]

*****************

c)

The standard error of the mean here is

sigma(Xbar) = sigma/sqrt(n)

= 50/sqrt(2500)

= 1 [ANSWER]