posted by holly on .
if you randomly answer a t/f test and want to figure the possibililty of gettng at least an 80......how do you start and then once you have done this, what if you want to try it 4 more times? HELP
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.