Stats Question

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Stats Question

Postby SomeFloridaKid » Wed Feb 22, 2017 1:49 am UTC

So I'm really quite awful at probability.
I have a homework problem (so i'm not asking for the answer, rather guidance on how to think about it)
A professor has a 20 question true/false reading quiz he's giving to his students. He wants to choose the passing grade such that there is less
than a .05 chance of a student who is just guessing can pass. What score should he set?

So I know it's binomial, the average score someone would get is a 50% with a standard deviation of sqrt(5).
Where do I go from there? Would I do 10 (number you get right on average) + 2 standard deviations for a 95% interval? Or am I missing something
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Re: Stats Question

Postby Xanthir » Wed Feb 22, 2017 2:26 am UTC

Overall, yes, but note that you want the 1-tail z score, because you want the 5% all at one end, not split between both ends. 2 stdevs is the 2-tail score.
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Re: Stats Question

Postby cyanyoshi » Wed Feb 22, 2017 2:36 am UTC

It looks like you are on the right track. Just be careful that for a 95% confidence interval, there is just a 2.5% chance of being at least 2 standard deviations above the mean. Do you see why?

Edit: Xanthir sees why :P

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Re: Stats Question

Postby MartianInvader » Wed Feb 22, 2017 8:15 pm UTC

Another way to do this problem, rather than using the normal approximation, is to just calculate the probabilities directly. You can use the formula for the binomial distribution to determine the chance that a student randomly guessing gets all 20 questions right, then add that to the chance of getting 19/20 questions right, and continue until you get something bigger than 5%.
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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