Dice rolled 15 times, results averaged; find prob. average is > 4.2

mathhelper123

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Need a bit of help with this one. I have tried my best to look through all the notes we were provided however I can seem to figure this one out.

a)
I roll a six-sided dice 15 times and average the results, what is the approximate probability that the average will be more than 4.2 (i.e. exceeding the 60% percentile)
b) Now I roll it 45 times, do you expect the chance will be higher, lower, or the same? What is the new probability
c) What about a single die roll? (beware cognitive inertia)

Thanks in advance!!!

 
Application of Central Limit Theorem

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For part b, change n from 15 to 45. For part c, change n to 1.
 

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