i need help with this asap pls

Suppose a random sample of size 30 is selected from a population with a = 8 . Find the value of the standard error of the mean in each of the following cases. (Use the finte poputation correction factor if appropriate. Round your answert to two decimal places.) (a) The population size is infinite. (b) The population size is N=30,000. (c) The population size is N=3,000. (d) The population size is N=300. You may need to use the appropriate appendix table or technology to answer this question. The Wall Stroet Journal reports that 33\% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on thair federal inconse tax return, The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard devation is a =$2,400. (a) What is the probsability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for each the following sample sizes: 30,50,100, and 300 ? (Round your answers to four dedimat places.) sample size n=30 aample size n=50 sample size n=100 sample size n=300 (b) What is the advantage of a larger sample size when attecipting to estimate the population mean? A larger sample has a standard error that is closer to the population standard deviation. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean. A larger sample lowers the population atandard deviation. A larger sample increases the probability that the sample mean will be a specified distance away from the population mean