here are a total of 50 multiple-choice questions. Each question carries 2 marks and the full mark of the exam is 100 marks. Each question has 3 possible answers and only one of them is correct. Assume that a student attempted the exam by random guessing the answer of each question. Correct your answers to 4 decimal places. Find the probability that the student obtains at most 6 marks given that the student gets at least 45 questions wrong.Answer in 4d.p. Use the normal distribution as an approximation to the binomial distribution to estimate the probability that the student gets more than 30 marks.Answer Use the result of (b) to estimate the probability that at least three out of 8 students who choose the answer to each question randomly will get more than 30 marks. You need to use the EXACT value that you obtained from (b) to
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
there are a total of 50 multiple-choice questions. Each question carries 2 marks and the full mark of the exam is 100 marks. Each question has 3 possible answers and only one of them is correct. Assume that a student attempted the exam by random guessing the answer of each question. Correct your answers to 4 decimal places.
- Find the
probability that the student obtains at most 6 marks given that the student gets at least 45 questions wrong.Answer in 4d.p. - Use the normal distribution as an approximation to the binomial distribution to estimate the probability that the student gets more than 30 marks.Answer
- Use the result of (b) to estimate the probability that at least three out of 8 students who choose the answer to each question randomly will get more than 30 marks. You need to use the EXACT value that you obtained from (b) to do this question. That is, do not use the rounded value to do this question.Answer
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Suppose a random sample of 22 is obtained from a population that isnormally distributed with mean 300 and variance 227. Find the probability that the sample standard deviation is larger than 110% of the population standard deviation. Correct your answer to 4 decimal places.
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