A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 28 weeks. Assume that the length of unemployment is normally distributed with population mean of 28 weeks and the population standard deviation of 8 weeks. Suppose you would like to select a random sample of 15 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 less than 25 weeks?
4. For 15 unemployed individuals, find the probability that the average time that they found the next job is less than 25 weeks.
5. For part d), is the assumption of normal necessary?Yes No