Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 28 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 28 weeks and that the population standard deviation is 2.7 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 28.2. P(X > 28.2) = (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n = 72 is randomly selected with a mean greater than 28.2. P(M > 28.2) =

Answer 1

First let us assume that, the numberof unemployment weeks is Normally distributed. Therefore,

if denotes the number of unemployment week of a randomly chosen individual, then,

Therefore,

where. is the distribution function of distribution and we have

Now, it is given that is the mean of a randomly chosen sample of size 72. Therefore, if we consider,

then,

Hence,

Now, . Therefore,