A population has a standard deviation of 97. We take a random sample of size 26 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 variance of this population?

b) What is the variance of Xbar? (to three decimal places)

c) What is the standard deviation of Xbar? (to three decimal places)

d) What is the variance of Xtot? (to three decimal places)

e) What is the standard deviation of Xtot? (to three decimal places)

f) What is the smallest sample size, n, which will make the standard deviation of Xtot at least 2589?

g) What is the smallest size sample, n, which will make the variance of Xtot at least 4,000,000?

h) Copy your R script for the above into the text box here.