If there is a test of 12 true false questions and all answers are guessed what is the mean and standard deviation of correct answers?

Answer 1

We'll assume reasonably that you get a correct answer with probability 0.5.

Then the context implies that the number of correct answers is a sum of 12 Bernoulli random variables with p=0.5, which becomes a Binomial distribution with n=12 and p=0.5. Formally:

Y(i)~Ber(0.5) => X = Y(1) + ... + Y(12) => X~Bin(12,0.5)

The mean for a Binomial distribution is n*p, hence E(X)=12*0.5=6.

The variance for a Binomial distribution is n*p*(1-p), hence Var(X)=12*0.5*0.5=3.

The standard deviation is calculated as the square root of the variance so SD(X)=3^0.5=1.732.