Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 9 weeks. Suppose you would like to select a random sample of 35 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 less than 27 weeks?
4. For 35 unemployed individuals, find the probability that the average time that they found the next job is less than 27 weeks.
5. For part d), is the assumption of normal necessary? NoYes

Answer 1

Solution :

Given that ,

mean = = 25

standard deviation = = 9

a.

X N (25 , 9)

b.

n = 35

= 25

= / n = 9 / 35 = 1.5213

N (25 , 1.5213)

c.

P(x < 27) = P[(x - ) / < (27 - 25) / 9]

= P(z < 0.22)

= 0.5871

Probability = 0.5871

c

P( < 27) = P(( - ) / < (27 - 25) / 1.5213)

= P(z < 1.31)

= 0.9049

Probability = 0.9049

d.

yes