Question

A population has a variance of 196, we take a random sample of size 15 from this population. Let Xbar be the sample mean, and let xtot be the sample sum of our sample. These are random variables. a) What is the standard deviation of this population? b) What is the varlance af Xbar? (to three decimal places) c) What is the standard deviation of Xbar? (to three decimal places) d) What is the standard deviation of Xtot? (to three decimal places) e) What is the smallest sample size, n, which will make the standard deviation of Xtot at least 87? f) What is the smallest size sample, n, which will make the variance of Xtot at least 5000?

Answer 1

a) std deviaiton =sqrt(196)=14

b)variance of X bar =196/15=13.067

c)std deviation of x bar =3.615

d)std deviation of x total =sqrt(196*15)=54.222

e)

sample size =(87²/196)=~39

f)

sample size =5000/196=26