Help needed on problem, URGENT! Thanks in advance.

#1
I'm stuck on figuring otu the mechanism required to solve these sample mean problems when you need to compare two different samples. Check it out...showing me the equation for figuring any of these out, especially c, would save me from further brain melting.

(11) Suppose that the IQ’s of East State University’s students are approximately normally distributed with mean 130 and standard deviation 8. Suppose that the IQ’s of West State University’s students are approximately normally distributed with mean 120 and standard deviation 10.

(a) If we select one student from each university, find the probability that the East State student’s IQ is at least 5 points higher than the West State student’s IQ.

(b) We select 3 West State students at random. Find the probability that their average IQ is at least 125.

(c ) We select 3 students from each school. Find the probability that the average IQ of the East State students is at least 5 points higher than the average for the West State students.
 
#2
Here is a hint for Part B.

The question asks:

(b) We select 3 West State students at random. Find the probability that their average IQ is at least 125.

Well, we need to set up our model, and the question has already provided us with what we need to do so....

Suppose that the IQ’s of West State University’s students are approximately normally distributed with mean 120 and standard deviation 10.

So we are dealing with the mean IQ, but not for one person, for 3. In this case what you will need to do is use the formula for finding the standard error, which is to take your known standard deviation, and divide it by the square root of the sample size, in this case 3.

We know the mean for our model already, it is 120. But for the average IQ of 3 people, we don't use the given Standarc Deviation, we use -- SD/Square Root of 3, which comes out to approximately 5.77

So you have for your model N(120, 5.77)

Now you can use your proposed mean of 125 and check it's probability against your model. Let me know if I can be of furher assistance.
 
#3
(a) If we select one student from each university, find the probability ....

Hi, I have tried part a. I do not want to post it yet to give others a chance to attempt it.

My result is 0.99461, can anyone confirm or reject this? I am not sure if my method is correct.

PeterVincent