Question

In: Statistics and Probability

A leading magazine (like Barron's) reported at one time that the average number of weeks an...

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.3 weeks and that the population standard deviation is 7.5 weeks. Suppose you would like to select a random sample of 124 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35.8 and 36.1. P(35.8 < X < 36.1) =

Find the probability that a sample of size n=124 is randomly selected with a mean between 35.8 and 36.1. P(35.8 < M < 36.1) =

Enter your answers as numbers accurate to 4 decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 36.3

standard deviation = = 15

a ) P (35.8 < x < 36.1 )

P ( 35.8 - 36.3 / 7.5) < ( x -  / ) < ( 36.1 - 36.3 / 7.5)

P ( -0.5 / 7.5 < z < - 0.2 / 7.5 )

P (-0.07 < z < - 0.03)

P ( z < - 0.03) - P ( z < -0.07)

Using z table

= 0.4880 - 0.4721

= 0.0159

Probability = 0.0159

b ) n = 124

=36.3

= / n = 7.5 124 = 37.94733

P (35.8 < M< 36.1 )

P ( 35.8 - 36.3 / 0.6735) < ( M - / ) < ( 36.1 - 36.3 / 0.6735)

P ( -0.5 / 0.6735 < z < - 0.2 / 0.6735 )

P (-0.74 < z < - 0.30)

P ( z < - 0.30) - P ( z < -0.74)

Using z table

= 0.3821- 0.2296

= 0.1525

Probability = 0.1525


Related Solutions

A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 17.2 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.2 weeks and that the population standard deviation is 8.1 weeks. Suppose you would like to select a random sample of 190 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 15.6 and 18.8....
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 33.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 33.9 weeks and that the population standard deviation is 4.9 weeks. Suppose you would like to select a random sample of 218 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.7 and 34.1....
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 40 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 40 weeks and that the population standard deviation is 3.2 weeks. Suppose you would like to select a random sample of 79 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is greater than 40.6. P(X...
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 88 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is greater than 39.6. P(X...
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 27 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 27 weeks and that the population standard deviation is 9 weeks. Suppose you would like to select a random sample of 32 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is less than 28. P(X...
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.3 weeks and that the population standard deviation is 7.5 weeks. Suppose you would like to select a random sample of 124 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 35.8 and 36.1....
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 9 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places. What is the distribution of XX? XX ~...
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 33 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 33 weeks and that the population standard deviation is 3 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is less than 34. P(X...
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 2 weeks. Suppose you would like to select a random sample of 39 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places. What is the distribution of XX? XX ~...
A leading magazine (like Barron's) reported at one time that the average number of weeks an...
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 2.5 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 28.5. P(X...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT