Barrons reported at one time that the average number of week

Barron\'s reported at one time that the average number of weeks an individual is unemployed is 32 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 32 weeks and that the population standard deviation is 2.2 weeks. Suppose you would like to select a random sample of 80 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 31.5. P(X > 31.5) =

Find the probability that a sampe of size n=80 is randomly selected with a mean greater than 31.5 P(M > 31.5)

Solution

Mean ( u ) =32
Standard Deviation ( sd )= 2.2 / Sqrt ( 80 )
Number ( n ) = 80
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 31.5) = (31.5-32)/2.2/ Sqrt ( 80 )
= -0.5/0.246= -2.0328
= P ( Z >-2.0328) From Standard Normal Table
= 0.979