M Gmail YouTube Maps YouTube Barron's reported that the average number of weeks an individual is unemployed is 16.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 16.5 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a sample of 50 unemployed individuals for a follow-up study. (a) Show the sampling distribution of x, the sample mean average for a sample of 50 unemployed individuals. weeks -1.8 -1.2 -0.6 0 0.6 1.2 1.8 weeks weeks 4.5 8.5 12.5 16.5 20.5 24.5 28.5 14.7 15.3 15.9 16.5 17.1 17.7 18.3 O weeks 48.2 48.8 49.4 50 50.6 51.2 51.8 O (b) What is the probability that a simple random sample of 50 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 probability that a simple random sample of 50 unemployed individuals will provide a sample mean within - week of the population mean? (Round your answer to four decimal places.)