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October 30, 2014

October 30, 2014

Posted by **holly** on Thursday, July 5, 2007 at 5:17pm.

Let N be the number of questions. You are asking for the probability of getting N/5 or fewer wrong by randomly guessing.

Assume N>> 1 and use an error-function approximation for the number of questions answered correctly. The mean will be N/2 and the standard deviation will be sqrt[N*p*(1-p)] = (1/2)sqrtN, since p = 1/2 is the probability of getting each one right.

Inegrate the probability of correct answers from 0.8 N to N, which you can treat as infinity when N is very large.

The larger the value of N, the less likely you will be to get 80% right.

For N=25, I get a standard deviation of 2.5 about a mean of 12.5, and the probability of getting 20 or more right will be 0.0013. It becomes a much lower probability of N = 100. You need to use an error function table for this sort of problem.

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