Suppose a random sample of size 50 is selected from a population with a = 12. Find the value of the standard error of the mean in each of the following cases. (Use the nite population correction factor if appropriate. Round your answers to two decimal places.) (a) The population size is infinite. [:1 (b) The population size is N = 50,000. [:1 (c) The population size is N = 5,000. :1 (d) The population size is N = 500. :1 You may need to use the appropriate appendix table or technology to answer this question. The Wall Street Journal reported that the mean amount of itemized deductions for the population of middle-income taxpayers was $16,642. Assume that the underlying population is normally distributed with a standard deviation of a = $2,400. (a) What is the probability 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 of the following sample sizes: 20, 60, 150, and 400? (Round your answers to four decimal places.) sample size n = 20 :] sample size n = 60 :] sample size n = 150 :] sample size n = 400 l:] (b) What is the advantage of a larger sample size when attempting to estimate the population mean? O A larger sample increases the probability that the sample mean will be a specified distance away from the population mean. 0 A larger sample lowers the population standard deviation. 0 A larger sample increases the probability that the sample mean will be within a specied distance of the population mean. O A larger sample has a standard error that is closer to the population standard deviation