You may need to use the appropriate appendix table or technology to answer this question. Barron's reported that the average number of weeks an individual is unemployed is 18.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 18.5 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a sample of 40 unemployed individuals for a followup study. (a) Show the sampling distribution of Z the sample mean average for a sample of 40 unemployed Individuals. weeks weeks weeks 1.8 1.2 0.6 0 0.6 1.2 1.8 16.7 17.3 17.9 18.5 19.1 19.7 20.3 38.2 38.8 39.4 40 40.6 41.2 41.8 0 (DO (D0 (D weeks 6.5 10.5 14.5 18.5 22.5 26.5 30.5 (D (b) What Is the proaability that a simple random sample of 40 unemployed Individuals will provide a sample mean within 1 week of the population mean? (Round your answer to four decimal places.) : (c) What is the proaability that a simple random sample of 40 unemployed individuals will provide a sample mean within % week of the population mean? (Round your answer to four decimal places.)