There were 8 questions on Exam I. Out of these, each student was allowed to choose...
There were 8 questions on Exam I. Out of these, each student was allowed to choose 2 questions for resubmission. Suppose students made their choices independently and randomly (i.e., each student chose 2 out of the 8 questions completely at random). What is the expected number of problems not chosen by any of the 70 students in the classroom?
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There were 8 questions on Exam I. Out of these, each student was
allowed to choose...
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)
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...
6. Two sections of a class contain 50 students each who just did a midterm exam....
6. Two sections of a class contain 50 students each who just did a midterm exam. In the first section 90% of the students passed the exam, in the second section only 70% of the students passed. Two friends randomly chose a sections at enrolment, but chose 1 the same one. Here we assume that we pick two students independently at random with replacement (so there is some chance that two students can end up being the same one). a....
Exercise 1.4. On a multiple-choice exam with four choices for each question, a student either knows...
Exercise 1.4. On a multiple-choice exam with four choices for each question, a student either knows the answer to a question or marks it at random. Suppose the student knows answers to 70% of the exam questions. If she marks the answer to question 1 correctly, what is the probability that she knows the answer to that question?
A student ran out of time on a multiple choice exam and randomly guessed the answers...
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d. e - and only one correct answer. What is the probability that she answered neither of the problems correctly?
3. Class rank. Choose a college student at random and ask his or her class rank...
3. Class rank. Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are as follows: Lowest 10% Rank: Probability: Top 20% 0.40 Second 20% 0.30 Third 20% 0.20 (a) What must be the probability that a randomly chosen student was in the bottom 40% of his or her high school class? (b) To simulate the class standing of randomly chosen students, how would you assign digits to represent th...
Question* On STAT your assessment is based on: Final Exam Learn based online assessment Assignments 4790 +' 3490 19% Consider three random variables X, Y and Z which respectively represent the ex...
Question* On STAT your assessment is based on: Final Exam Learn based online assessment Assignments 4790 +' 3490 19% Consider three random variables X, Y and Z which respectively represent the exam, online assessment total and assignment scores (out of 100%) of a randomly chosen student. Assume that X, Y and Z are independent (this is clearly not true, but the answers may be a reasonableapproximation).Suppose that past experience suggests the following properties of these assessment items (each out of...
On stat your assessment is based on: Final Exam 47% Learn based on‐line assessment 34% Assignments...
On stat your assessment is based on: Final Exam 47% Learn based on‐line assessment 34% Assignments 19% Consider three random variables X, Y and Z which respectively represent the exam, on‐line assessment total and assignment scores (out of 100%) of a randomly chosen student. Assume that X, Y and Z areindependent (this is clearly not true, but the answers may be a reasonable approximation). Suppose that past experience suggests the following properties of these assessment items (each out of 100%):...
3) Suppose a student is taking a multiple-choice question exam in which each answer has four...
3) Suppose a student is taking a multiple-choice question exam in which each answer has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on the following strategy: She will place four balls marked A, B, C, and D in a box. She randomly selects one ball for each question and replaces the ball in the box after marking the letter of the ball as the answer. If there...
QUESTION 2 Exercises 19.8 and 19.10 Choose a college student at random and ask his or...
QUESTION 2 Exercises 19.8 and 19.10 Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are as follows: Rank top 20% second 20% third 20% lowest 40% Probability 0.40 0.30 0.20 What must be the probability that a randomly chosen student was in the bottom 40% of his or her high school class? A. Assign the digits as follows: 0-4 represent top 20%; 0-3 represent second 20%; 0-2 represent...
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)
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...
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d. e - and only one correct answer. What is the probability that she answered neither of the problems correctly?
3. Class rank. Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are as follows: Lowest 10% Rank: Probability: Top 20% 0.40 Second 20% 0.30 Third 20% 0.20 (a) What must be the probability that a randomly chosen student was in the bottom 40% of his or her high school class? (b) To simulate the class standing of randomly chosen students, how would you assign digits to represent th...
Question* On STAT your assessment is based on: Final Exam Learn based online assessment Assignments 4790 +' 3490 19% Consider three random variables X, Y and Z which respectively represent the exam, online assessment total and assignment scores (out of 100%) of a randomly chosen student. Assume that X, Y and Z are independent (this is clearly not true, but the answers may be a reasonableapproximation).Suppose that past experience suggests the following properties of these assessment items (each out of...
QUESTION 2 Exercises 19.8 and 19.10 Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are as follows: Rank top 20% second 20% third 20% lowest 40% Probability 0.40 0.30 0.20 What must be the probability that a randomly chosen student was in the bottom 40% of his or her high school class? A. Assign the digits as follows: 0-4 represent top 20%; 0-3 represent second 20%; 0-2 represent...
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