Question

Barron's reported that the average number of weeks an individual is unemployed is 21.5 weeks. Assume...

Barron's reported that the average number of weeks an individual is unemployed is 21.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 21.5 weeks and that the population standard deviation is 5.5 weeks. Suppose you would like to select a sample of 65 unemployed individuals for a follow-up study. Use z-table.

What is the probability that a simple random sample of 65 unemployed individuals will provide a sample mean within 1 week of the population mean? (to 4 decimals)

What is the probability that a simple random sample of 65 unemployed individuals will provide a sample mean within 1/2 week of the population mean? (to 4 decimals)

Homework Answers

Answer #1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ= 21.5
std deviation   =σ= 5.5000
sample size       =n= 65
std error=σ=σ/√n= 0.6822

probability that a simple random sample of 65 unemployed individuals will provide a sample mean within 1 week of the population mean:

probability = P(20.5<X<22.5) = P(-1.47<Z<1.47)= 0.9292-0.0708= 0.8584

2)

probability that a simple random sample of 65 unemployed individuals will provide a sample mean within 1/2 week of the population mean:

probability = P(21<X<22) = P(-0.73<Z<0.73)= 0.7673-0.2327= 0.5346
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Barron's reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume...
Barron's reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 5 weeks. Suppose you would like to select a sample of 50 unemployed individuals for a follow-up study. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of...
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 15.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 15.5 weeks and that the population standard deviation is 9.1 weeks. Suppose you would like to select a random sample of 11 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 9.7 and 12.2....
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 32 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 32 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 51 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is greater than 31.3. 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 35 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 35 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 39 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 36 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36 weeks and that the population standard deviation is 3 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 35. 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 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...
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 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 6.2 weeks. Suppose you would like to select a random sample of 156 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 28.7 and 29.8....
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 39.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39.5 weeks and that the population standard deviation is 9.3 weeks. Suppose you would like to select a random sample of 172 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 37.4 and 39.3....
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 20.2 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 20.2 weeks and that the population standard deviation is 6.8 weeks. Suppose you would like to select a random sample of 201 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 20.8 and 20.9....
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 15.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 15.3 weeks and that the population standard deviation is 8 weeks. Suppose you would like to select a random sample of 169 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 13.8 and 14.5....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT