Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 14.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 14.9 weeks and that the population standard deviation is 6.2 weeks. Suppose you would like to select a random sample of 208 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 14.7 and 16.1.
P(14.7 < X < 16.1) =

Find the probability that a sample of size n=208 is randomly selected with a mean between 14.7 and 16.1.
P(14.7 < M < 16.1) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Since the distribution is normal hence Z score will be applicable for probability calculation here so,

a) P(14.7 < X < 16.1)

start with calculating the Z value at give X points as

and Z at X=16.1

P(14.7 < X < 16.1) =P(-0.03<Z<0.19) is computed using Z table shown below as

=0.5733-0.4880

=0.0853

b) P(14.7 < X < 16.1) id 208 is selected , the Z score would be

and Z at mean =16.1

P(14.7 < X < 16.1)=P(-0.47<Z<2.79) , using Z table shown below:

=0.9974-0.3192

=0.6782