Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 12.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 12.3 weeks and that the population standard deviation is 5.5 weeks. Suppose you would like to select a random sample of 99 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 13.7 and 14. P ( 13.7 < x < 14 ) = Find the probability that a sample of size n = 99 is randomly selected with a mean between 13.7 and 14. P ( 13.7 < ¯ x < 14 ) = Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Mean length of unemployment for the population of unemployed individual is :

standard deviation:

The probability for a randomly selected single individual :

To calculate this we need to find the Z-score,

Given:

Z-score for x=13.7:

Z-score for x=14:

                                   

   Or 2.09%                                

So, the probability that a randomly selected single individual has a unemployment between 13.7 and 14 weeks is 0.0209 Or 2.09%

Now if a random sample of unemployed individual has taken, then we need to find the probability that the sample mean( mean length of unemployment) is between 13.7 and 14 weeks, i.e.,

Z-score for :

Z-score for

                                  

                                   

                                    Or 0.46%

So, the probability for a randomly selected sample of unemployed individual of 99 has a sample mean in between 13.7 and 14 is 0.0046 Or 0.46%