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(3) (15 pts) Suppose that in the State of Nebraska the written exam for a drivers...
(3) (15 pts) Suppose that in the State of Nebraska the written exam for a drivers...
(3) (15 pts) Suppose that in the State of Nebraska the written exam for a drivers license consists of 4 multiple-choice questions. Each question has 4 possible choices, only one of which is correct. Passing requires answering at least 3 questions correctly. Consider an experiment: an uninformed student-driver guesses at random on each question, where "guessing at random" means that (i) the student answers each question independently of the other questions and (ii) that for each question the student chooses...
l6 pts] Suppose that in the Province of Ontario the written cxam for a drivers license...
l6 pts] Suppose that in the Province of Ontario the written cxam for a drivers license consists ot 4 multiple-choice questions. Each question has 4 possible choices, denoted a,b,cd, only one of which is correct. Fo the sake of simplicity, you may assume throughou ts exerse tha the corret answer is "a for all four quesions, but that a shudent does not know this before taking the exam. Passing requires answering at least 3 queslions correclly. Consider an experiment defined...
onsider an exam which has n multiple choice questions. Each question has k possible answers, among...
onsider an exam which has n multiple choice questions. Each question has k possible answers, among which only one answer is correct. (a) Consider a student who chooses at random the answers for all questions of the exam. Let X be the number of correct answers of this student. What is distribution of X? What is the expected value of X? (b) To eliminate the effect of guessing, the instructor decides to mark the according to the following rule: for...
1. On a multiple choice exam with 4 possible answers for each of 7 questions, what...
1. On a multiple choice exam with 4 possible answers for each of 7 questions, what the probability that a student will get 6 or more correct just by guessing randomly? (Hint: the student has an independent 1/4 chance of answering each individual question successfully.)
5. A student takes a multiple-choice exam where each question has 5 possible answers. He works...
5. A student takes a multiple-choice exam where each question has 5 possible answers. He works a question correctly if he knows the answer, otherwise he guesses at random. Suppose he knows the answer to 80% of the questions. (a) What is the probability that on a question chosen at random the student gets the correct (b) Given that the student gets the correct answer to this question, what is the probability answer? that he actually knew the answer?
r=3 QUESTION 16 5 poin Suppose a multiple choice exam has 47 questions with 7 answer...
r=3 QUESTION 16 5 poin Suppose a multiple choice exam has 47 questions with 7 answer choices per question, only one of which is correct. Suppose a student randomly guesses on every question of the exam, and let X be the number of correct answers out of the total number of questions. What is E(X), that is, the expected number of correct answers, if we assume X has a binomial distribution, to one decimal place?
Suppose you gave a multiple-choice exam with 16 questions on it. Each question has 4 alternatives....
Suppose you gave a multiple-choice exam with 16 questions on it. Each question has 4 alternatives. What is the probability that a student who guesses at random on each of the 16 questions will score 6 or more correct answers? Assume that each alternative to each question is equally likely to be chosen. A. P=0.9999 B. P=0.8770 C. P=0.0123 D. P<0.001 Please help and show work. Thank you.
22. A true-false exam has 54 questions. Use the CLT to approximate the probabil- ity of getting a passing score of 35 o...
22. A true-false exam has 54 questions. Use the CLT to approximate the probabil- ity of getting a passing score of 35 or more correct answers simply by guessing on each question. 6.7.1 Theorem (Central Limit Theorem). Let X1, X2, ... be an infinite se- quence of iid random variables with mean u and standard deviation o, and let Sn = 21–1 X;. Then lim P(Some < x) = P(x). (6.7) It follows that lim P (as so o) =...
Question 13 0.2 pts Suppose you are taking a multiple choice exam with 55 questions, each...
Question 13 0.2 pts Suppose you are taking a multiple choice exam with 55 questions, each with 4 possible answers. If you were to guess at random for each question, how many questions would you expect to get right? Your answer does not need to be an integer. Question 14 0.2 pts On average 1.8 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?
1. Suppose that the length of time a particular type of battery lasts follows an exponential...
1. Suppose that the length of time a particular type of battery lasts follows an exponential distribution with a mean of 25.0 days. Find the probability that the average time a sample of 49 batteries lasts is at most 24.7 days a. 0.4665 b. 0.3723 c. 0.6277 d. 0.5335 2. Suppose that the length of time a particular type of battery lasts follows an exponential distribution with a mean of 25.0 days. Suppose the length of time a battery lasts...
(3) (15 pts) Suppose that in the State of Nebraska the written exam for a drivers license consists of 4 multiple-choice questions. Each question has 4 possible choices, only one of which is correct. Passing requires answering at least 3 questions correctly. Consider an experiment: an uninformed student-driver guesses at random on each question, where "guessing at random" means that (i) the student answers each question independently of the other questions and (ii) that for each question the student chooses...
l6 pts] Suppose that in the Province of Ontario the written cxam for a drivers license consists ot 4 multiple-choice questions. Each question has 4 possible choices, denoted a,b,cd, only one of which is correct. Fo the sake of simplicity, you may assume throughou ts exerse tha the corret answer is "a for all four quesions, but that a shudent does not know this before taking the exam. Passing requires answering at least 3 queslions correclly. Consider an experiment defined...
onsider an exam which has n multiple choice questions. Each question has k possible answers, among which only one answer is correct. (a) Consider a student who chooses at random the answers for all questions of the exam. Let X be the number of correct answers of this student. What is distribution of X? What is the expected value of X? (b) To eliminate the effect of guessing, the instructor decides to mark the according to the following rule: for...
1. On a multiple choice exam with 4 possible answers for each of 7 questions, what the probability that a student will get 6 or more correct just by guessing randomly? (Hint: the student has an independent 1/4 chance of answering each individual question successfully.)
5. A student takes a multiple-choice exam where each question has 5 possible answers. He works a question correctly if he knows the answer, otherwise he guesses at random. Suppose he knows the answer to 80% of the questions. (a) What is the probability that on a question chosen at random the student gets the correct (b) Given that the student gets the correct answer to this question, what is the probability answer? that he actually knew the answer?
r=3 QUESTION 16 5 poin Suppose a multiple choice exam has 47 questions with 7 answer choices per question, only one of which is correct. Suppose a student randomly guesses on every question of the exam, and let X be the number of correct answers out of the total number of questions. What is E(X), that is, the expected number of correct answers, if we assume X has a binomial distribution, to one decimal place?
22. A true-false exam has 54 questions. Use the CLT to approximate the probabil- ity of getting a passing score of 35 or more correct answers simply by guessing on each question. 6.7.1 Theorem (Central Limit Theorem). Let X1, X2, ... be an infinite se- quence of iid random variables with mean u and standard deviation o, and let Sn = 21–1 X;. Then lim P(Some < x) = P(x). (6.7) It follows that lim P (as so o) =...
Question 13 0.2 pts Suppose you are taking a multiple choice exam with 55 questions, each with 4 possible answers. If you were to guess at random for each question, how many questions would you expect to get right? Your answer does not need to be an integer. Question 14 0.2 pts On average 1.8 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?
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