Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 23 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 23 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 72 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 23.2.
P(X > 23.2) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n=72n=72 is randomly selected with a mean greater than 23.2.
P(M > 23.2) =  (Enter your answers as numbers accurate to 4 decimal places.)

Answer 1

Here population standard deviation is given hence we will use normal distribution

Also it is given that mean is 23 and standard deviation is 2

Now we need to find

As population is normal we can convert x to z

Now as population is normal as per central limit theorem sample mean is also normal with mean= and standard deviation is

Now we need to find , as sample mean is normally distributed we can convert M to z.