On the Swedish SAT test, you have 5 options for every question where precisely one option is correct. If you answer randomly, what is the probability that your score will be 0.9 if the maximum score is 2.0 and the results are normally distributed?
Attempt: The mean should be 1.0. Then how do we know standard deviation from our information so that we can compute?
The probability that any question is answered correctly is $p=0.2$. If the number of questions is $N=180$, the number you get right is $n$ and the maximum score $S_{max}=2$ your score is $s=\frac{n}{N}\times S_{max}$.
Now $n\sim B(N,p)$, that is the number of correct answers has a binomial distribution with the given parameters. Then using the Normal approximation to the Binomial distribution we have $n \mbox{ approximately} \sim N(Np,Np(1-p))$, and so your score has approximate normal distribution with mean $p\times S_{max}$ and standard deviation $\sqrt{\frac{p(1-p)}{N}}\times S_{max}$