probability of obtaining a sample mean...

[jolu606]

Hi Everyone, I hope someone can help me with these two problems...I know how to find the z score but not sure what part it plays in this. I think if I knew where to start I could get this...

14) The population of IQ scores forms a normal distribution with a mean of µ=100 and a standard deviation of ? =15. What is the probability of obtaining a sample mean greater than M=105,

a. for a random sample of n=9 people?

b. for a random sample of n=36 people?

16) A population of scores forms a normal distribution with a mean of µ=40 and a standard deviation of ? =12.

a. What is the probability of randomly selecting a score less than X =34?

b. What is the probability of selecting a sample of n=9 scores with a mean of less than M=34?

c. What is the probability of selecting a sample of n=36 scores with a mean of less than M=34?

 

[wjm11]

14) The population of IQ scores forms a normal distribution with a mean of µ=100 and a standard deviation of ? =15. What is the probability of obtaining a sample mean greater than M=105,

a. for a random sample of n=9 people?

b. for a random sample of n=36 people?

The standard deviation of the sample is equal to the standard deviation of the population divided by the square root of the sample size. Use the sample standard deviation to calculate your z value.

16) A population of scores forms a normal distribution with a mean of µ=40 and a standard deviation of ? =12.

a. What is the probability of randomly selecting a score less than X =34?

In this case, your sample size is one, so just use the population standard deviation.

b. What is the probability of selecting a sample of n=9 scores with a mean of less than M=34?

Use the sample std. dev., calculated using n = 9.

 

[jolu606]

Thanks, I didn't know how to get that standard deviation for the sample. Actually I didn't know I needed a different standard deviation for the random sample. How do I calculate the probability of obtaining that 105 mean though? does the p(A) formula come in somewhere? - jolu

 

[wjm11]

I didn't know how to get that standard deviation for the sample. Actually I didn't know I needed a different standard deviation for the random sample.

The principals involved here are very important to the understanding of statistical inference. I strongly encourage you to spend some time studying the "central limit theorem" and how it relates to the "sample standard deviation". If you happen to be using the book "The Practice of Statistics", 2nd edition, by Yates, Moore, and Starnes, please read chapters 9 and 10. An online search will also turn up many sources of information.

 

[jolu606]

Thank you. I'll post back if I make any progress.