A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that the length of unemployment is normally distributed with population mean of 29 weeks and the population standard deviation of 4 weeks. Suppose you would like to select a random sample of 16 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected individual found a job more than 27 weeks?

Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that the length of unemployment is normally distributed with population mean of 29 weeks and the population standard deviation of 4 weeks. Suppose you would like to select a random sample of 16 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places.

  1. What is the distribution of XX? XX ~ N(,)
  2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
  3. What is the probability that one randomly selected individual found a job more than 27 weeks? 

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