A large population of music stores is to be sampled. Theft amount per two-week period for any one music store, X, is assumed normally distributed with a mean theft amount per store of $500 and a standard deviation of $8.
(a) Calculate the mean and standard deviation of the sample mean based on data from 100 stores.
(b) What is the probability the sample average is within $1.80 of $500(based on 100 stores)?
(c) Would the probability in (b) be increased by .1 if the sample size were increased by 10% to n=110? Why or why not?
(d) Would the probability in (b) be affected substantially if the population standard deviation were $18 for n=100 stores? Why or why not?