Question

In: Statistics and Probability

2.   A student is taking a multiple-choice test in which each question has five choices. Assume...

2.   A student is taking a multiple-choice test in which each question has five choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place five balls (marked A, B, C, D and E) into a box. She randomly selected one ball for each question and replaces the ball in the box. The marking on the will determine her answer to the question. There are 6 multiple-choice questions on the test. What is the probability that she will correctly answer the following:

  1. five questions correct?
  1. at most three questions correct?

Solutions

Expert Solution


Related Solutions

A multiple-choice test has 6 questions. There are 4 choices for each question. A student who...
A multiple-choice test has 6 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly with a Probability of success = p =.25. Let X represent the number of correct answers out of six questions. (i) Use binomial distribution to complete the table (ii) Find the probability that the student will be successful in at least 4 questions. (iii) Find the probability that the student will be...
1. On a multiple choice test where each question has 4 choices of which only one...
1. On a multiple choice test where each question has 4 choices of which only one is correct you get 1.8 points for a correct answer and you lose .75 points for an incorrect answer. You lose no points nor gain any points if you leave the problem blank. We let the random variable x = points earned from guessing on a question. a) Find the probability distribution for x b) Is guessing a good idea if you cannot eliminate...
A multiple-choice test has 48 questions, each with four response choices. If a student is simply...
A multiple-choice test has 48 questions, each with four response choices. If a student is simply guessing at the answers, 1. What is the probability of guessing correctly for any individual question? 2. On average, how many questions would a student answer correctly for the entire test? 3. What is the probability that a student would get more than 15 questions correct? p(more than 15 answers correct) 4. What is the probability that a student would get 15 or more...
1. A student takes a 12 question multiple choice test. There are 5 answer choices, and...
1. A student takes a 12 question multiple choice test. There are 5 answer choices, and the student guesses on all the questions. What is the probability the student will get exactly 7 questions correct in order to pass? Round to 5 decimal places. a. 0.00332 b. 0.00587 c. 0.08304 d. 0.00213 2. If the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 5 defective parts from a sample of 100?...
A multiple choice test consists of 8 items each with 4 choices. A student guesses the...
A multiple choice test consists of 8 items each with 4 choices. A student guesses the answers by choosing an answer at random. Compute the probability that (a) the student answers all questions incorrectly? (b) the student answers all questions correctly? (c) the student answers 2 or more correctly? (d) Suppose the student is able to eliminate one of the answers as incorrect and chooses randomly from the other three choices. What is the probability the student answers 2 or...
For each question on a multiple-choice test, there are five possible answers of which exactly one...
For each question on a multiple-choice test, there are five possible answers of which exactly one is correct for each question. Assume there are 10 questions on the test and a student selects one answer for each question at random. Let X be the number of correct answers he or she gets. a) How is X distributed? (Specify the values of the corresponding parameters). b) Find P(X < 6) and P(X = 6). c) Find E(X) and V ar(X). 2....
27. A single multiple-choice question has 5 choices, only one of which is correct. A student...
27. A single multiple-choice question has 5 choices, only one of which is correct. A student taking this test knows the answer with probability 0.8. If the student does not know the answer, he or she guesses randomly. a) Find the probability that the student knew the answer, given that the question was answered correctly. b) To pass the test a student must answer at least eight questions correctly from ten, what is the probability that the student will pass...
A multiple-choice examination consists of 20 questions. Each question has five choices, labeled A, B, C,...
A multiple-choice examination consists of 20 questions. Each question has five choices, labeled A, B, C, D and E. All data for that exam is stored in a file exam.txt. The first line of data contains the correct answers to the twenty questions in the first 20 consecutive (one after the other) character positions. For Example: BECDCBAADEBACBEDDBED Each subsequent line in the file contains the answers for a single candidate. Data on a line consists of a candidate number (an...
A student is given 20 multiple choice questions. Each multiple choice question has 4 options &...
A student is given 20 multiple choice questions. Each multiple choice question has 4 options & only one correct answer. The student answers all the questions in a random manner. a) What is the probability the student scores 80% or above? b) What is the probability the student scores 50% or above?
Suppose you take a 30 question test, multiple choice, with each question having 4 choices. A,...
Suppose you take a 30 question test, multiple choice, with each question having 4 choices. A, B, C, D. If you randomly guess on all 30 questions, what is the probability you pass the exam (correctly guess on 60% or more of the questions)? Assume none of the questions have more than one correct answer. b) what the expected number of correct guesses? what is the standard deviation? c) what would be considered an unusual number of correct guesses on...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT