A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 27 weeks. Assume that the length of unemployment is normally distributed with population mean of 27 weeks and the population standard deviation of 5 weeks. Suppose you would like to select a random sample of 11 unemployed individuals for a follow-up study.Round the answers of following questions to 4 decimal places.

1. What is the distribution ofX?X~ N(,)
2. What is the distribution ofX?X~ N(,)
3. What is the probability that one randomly selected individual found the next job is more than 26 weeks?
4. For 11 unemployed individuals, find the probability that the average time that they found the next job is more than 26 weeks.
5. For part d), is the assumption of normal necessary?Yes No