An instructor gives her class the choice to do 8 questions out of the 11 on...
An instructor gives her class the choice to do 8 questions out of the 11 on an exam. (a) How many choices does each student have? (b) How many choices does a student have if he/she must answer at least 4 of the first 6 questions?
If 9 teachers are to be divided among 5 schools. (a) How many divisions are possible? (b) What if each school must receive two teachers?
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An instructor gives her class the choice to do 8 questions out
of the 11 on...
An instructor gives an exam with twelve questions. Students are allowed to choose any nine to...
An instructor gives an exam with twelve questions. Students are allowed to choose any nine to answer. (a) How many different choices of nine questions are there? (b) Suppose five questions require proof and seven do not. (i) How many groups of nine questions contain three that require proof and six that do not? (ii) How many groups of nine questions contain at least one that requires proof? (iii) How many groups of nine questions contain at most three that...
15. An instructor gives an exam with fourteen questions. Students are allowed to choose any ten...
15. An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer. a. How many different choices of ten questions are there? [4 points) b. Suppose the instructions specify that either both questions 1 & 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there? [4 points)
(1 point) An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection or 7 of them. If a student has figured out how to do 12 of the...
(1 point) An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection or 7 of them. If a student has figured out how to do 12 of the problems, what is the probability the he or she will answer correctly (a) all 7 problems? (b) at least 6 problems?
(1 point) An instructor gives his class a set of 18 problems with the information that the next...
An instructor gives his class a set of 16 problems with the information that the next...
An instructor gives his class a set of 16 problems with the information that the next quiz will consist of a random selection of 6 of them. If a student has figured out how to do 11 of the problems, what is the probability that he or she will answer correctly A) all 6 problems? B) at least 5 problems?
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...
A student is taking a multiple-choice exam in which each question has four choices. Assume that...
A student is taking a multiple-choice exam in which each question has four 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 four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There...
7. A statistics instructor wants to figure out how long it will take her students, on...
7. A statistics instructor wants to figure out how long it will take her students, on average, to complete an exam She believes that completion time should follow an exponential distribution with mean λ. She collects data from 10 randomly selected students, and the class meets for 50 minutes. (a) What are the appropriate hypotheses in this case? Explain your reasoning. (b) The instructor opts to use a signficance level of 0.10. In the context of the scenario, what does...
. There are n questions on a multiple choice exam, and for each question, there are...
. There are n questions on a multiple choice exam, and for each question, there are four choices. To pass the exam, one must correctly answer at least 70% of the questions. The student has not studied, so he/she has to resort to guessing on every question. a. Find the probability of the student passing for n = 10. b. Find the expected number of questions answered correctly for n = 20. c. Find the variance for the number of...
4. Consider a chessboard, shown below. At starting at the square al (the lower right hand...
4. Consider a chessboard, shown below. At starting at the square al (the lower right hand corner), you can go one step up or one step right at each move. The procedure stops until the point h8 (the upper right corner) is reached. a) How many different paths from al to h8 are possible? (b) How many differnt paths from al to h8 are possible if each path must pass through the square e4? 5. If 10 new teachers are...
A student is taking a multiple-choice exam in which each question has four choices. Assume that...
A student is taking a multiple-choice exam in which each question has four 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 four balls (marked A,B,C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five...
An instructor gives an exam with twelve questions. Students are allowed to choose any nine to answer. (a) How many different choices of nine questions are there? (b) Suppose five questions require proof and seven do not. (i) How many groups of nine questions contain three that require proof and six that do not? (ii) How many groups of nine questions contain at least one that requires proof? (iii) How many groups of nine questions contain at most three that...
15. An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer. a. How many different choices of ten questions are there? [4 points) b. Suppose the instructions specify that either both questions 1 & 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there? [4 points)
(1 point) An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection or 7 of them. If a student has figured out how to do 12 of the problems, what is the probability the he or she will answer correctly (a) all 7 problems? (b) at least 6 problems?
(1 point) An instructor gives his class a set of 18 problems with the information that the next...
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...
7. A statistics instructor wants to figure out how long it will take her students, on average, to complete an exam She believes that completion time should follow an exponential distribution with mean λ. She collects data from 10 randomly selected students, and the class meets for 50 minutes. (a) What are the appropriate hypotheses in this case? Explain your reasoning. (b) The instructor opts to use a signficance level of 0.10. In the context of the scenario, what does...
4. Consider a chessboard, shown below. At starting at the square al (the lower right hand corner), you can go one step up or one step right at each move. The procedure stops until the point h8 (the upper right corner) is reached. a) How many different paths from al to h8 are possible? (b) How many differnt paths from al to h8 are possible if each path must pass through the square e4? 5. If 10 new teachers are...
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