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The scores of a final exam have a Normal Distribution with mean $75$ and standard deviation 6. An independent sample size of $9$ is drawn from this distribution. The corresponding random variables are denoted as $X_1, \cdots X_9$

1) The probability that the sample mean $ \overline X$ lies between $74$ and $77$ is ...

2) In order to get an A, you need to be in the top $5$ percentile of the class. What is the minimum score you need to achieve an A ...

3) What is the probability that no one in the class obtains an A? ...

Answers:

1) $0.5328$

2) $84.87$

3) $\text{Not sure}$

Can someone help walk through the solution?

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1  
What are your personal thoughts on these three questions? –  Did Feb 5 '13 at 17:12
    
How would u do 1) seems to me like u need to use score but I'm not sure –  user61049 Feb 5 '13 at 18:19
    
Is this supposed to answer the query in my previous comment? –  Did Feb 5 '13 at 18:25
    
Seems like u should use z-score (my answer got cutoff) –  user61049 Feb 5 '13 at 18:26
2  
Sure. Back to square one: What are your personal thoughts on these three questions? –  Did Feb 5 '13 at 22:13

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