Question

A multiple choice test consists of 100 questions. Each question has 5 possible answers, only one of which is correct. Four points are awarded for each correct answer, and 1 point is taken off for each wrong answer. Suppose you answer all the questions by guessing at random, independently of all other questions
- What is the chance that you get more than 30 points?

Answer 1

If 26 questions are answered correctly and 74 questions are given wrong answers the score will be 30. Therefore at least 27 questions must be answered correctly to get more than 30 points.
From the Normal approximation to the binomial distribution:
The mean = np = 100 * 0.2 = 20
The standard deviation is given by
\[\sqrt{np(1-p)}=\sqrt{100\times 0.2\times 0.8}=4\]
The z-score for 26 using the continuity correction is
\[\frac{26-20+0.5}{4}=1.625\]
From a standard Normal distribution table the probability of answering up to 26 questions correctly is 0.9479. Therefore the probability of answering at least 27 questions correctly is given by 1.0000 - 0.9479

Answer 2

pls post clear ans

Answer 3

ans: 0.0558