SOLUTION: I am working my statistics class, and am having issues finding the correct formula for finding the following: The average diameter of certain Euro coins is a number in millimete

Question 314033: I am working my statistics class, and am having issues finding the correct formula for finding the following:
The average diameter of certain Euro coins is a number in millimeters with a standard deviation of a number in millimeters. If 9 coins are chosen at random, find the probability that the average diameter of those coins is more than a number in millimeters. Assume that the variable is normally distributed.
I have been using the following formula, but it is not working right, because I'm not sure what to do with the 9 coins:
z = Value - mean / standard deviation
I did not want you to work the problem for me, I just need assistance without getting the answer.
Thank You in advance...Rosanna
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I am working my statistics class, and am having issues finding the correct formula for finding the following:
The average diameter of certain Euro coins is a number in millimeters with a standard deviation of a number in millimeters.
---
Let assume average = u and the standard deviation is s.
---------------------------------
If 9 coins are chosen at random, find the probability that the average diameter of those coins is more than a number (k) in millimeters.
---------------------------------
Assume that the variable is normally distributed.
I have been using the following formula, but it is not working right, because I'm not sure what to do with the 9 coins:
----
The Central Limit Theorem guarantees
1. the mean of ALL the sample means of size 9 is u (the same mean as the population.
BUT
2. the std of ALL the samples of size 9 is s/sqrt(n) where n is the sample size.
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So your formula should be:

z = (Value - mean) / [standard deviation/sqrt(9)]
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Cheers,
Stan H.
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