Question

1.) A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 29.8 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 29.8 weeks and that the population standard deviation is 5.9 weeks. Suppose you would like to select a random sample of 194 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 29.1 and 30.2.
P(29.1<x<30.2)= ___?

Find the probability that a sample of size n=194n=194 is randomly selected with a mean between 29.1 and 30.2.
P(29.1<¯x<30.2)= ___?

2.) Scores for a common standardized college aptitude test are normally distributed with a mean of 500 and a standard deviation of 98. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 583.3.
P( xx > 583.3) =  

If 5 of the men are randomly selected, find the probability that their mean score is at least 583.3.
P( ¯xx¯ > 583.3) =  

Answer 1

Solution: 1.) A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 29.8 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 29.8 weeks and that the population standard deviation is 5.9 weeks. Suppose you would like to select a random sample of 194 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 29.1 and 30.2.

Answer: We are given:

We have to find:

When , we have:

rounded to two decimal places.

When , then we have:

rounded to two decimal places.

Therefore we have to find

Now using the standard normal table, we have:

Find the probability that a sample of size n=194 is randomly selected with a mean between 29.1 and 30.2.

Answer: We have to find here:

When , we have:

rounded to two decimal places.

When , then we have:

rounded to two decimal places.

Therefore we have to find

Now using the standard normal table, we have:

2.) Scores for a common standardized college aptitude test are normally distributed with a mean of 500 and a standard deviation of 98. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 583.3.

Answer: We are given:

We have to find here:

  

  

we have to find

Using the standard normal table we have:

If 5 of the men are randomly selected, find the probability that their mean score is at least 583.3.

Answer: We have to find .

When , then we have:

  

  

we have to find

Using the standard normal table we have: