I was giving an exam once. There were 60 questions and all had one correct answer out of four given options. I wasn't able to solve even a single question. So, I decided to guess.

But there was a problem. Professor said every wrong answer would add -1 mark to the final score and every correct answer would add +4 marks to the score. I looked at the exam with amazement and notice in each question professor has set 2 stupid options which were easy to eliminate. I eliminated all the 2 stupid options from all the 60 question.

Then I decided to guess all the 60 questions from the remaining 2 options left from all questions. Assuming that Professor is equally likely to set any of the options A, B, C or D as the correct answer, I did the math and found out I would get \(4\times60\times\frac{1}{2} - 60\times\frac{1}{2} = 90\) marks on average if I decide to guess all the questions. I was delighted.

But I want to know more. I want to find \(a\) and \(b\) such that I can be 90% sure that my marks would lie between \(a\) and \(b\).

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