You are to take a multiple-choice exam consisting of 100 questions with five possible responses to...

You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let r.v. X represent the number of correct responses on the exam.

(a). Specify the probability distribution of X.
(b. What is your expected number of correct responses?
(c). What are the values of the variance and standard deviation of X?
(d). What is the probability that you will get exactly the expected number of correct responses?

Solutions

Expert Solution

For further queries, please comment below.

Thank you.

milcah answered 4 months ago

Next > < Previous

Related Solutions

There are 100 multiple-choice question on exam, each having responses a, b, c, d. Suppose that...

There are 100 multiple-choice question on exam, each having responses a, b, c, d. Suppose that a student has a 70% chance to answer each question correctly, and all the answers are independent. If the student needs to answer at least 40 questions to pass, what is the probability that the student passes? Use normal approximation.

A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you...

A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 8 out of 12 questions correctly. What is the chance of this, if ; a. You go into the exam without knowing a thing, and have to resort to Pure guessing? b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices....

A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one...

A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one of which is correct. Four points are awarded for each correct answer. To discourage guessing, one point is taken away for every answer that is not correct (this includes answers that are missing). The company that creates the test has to understand how well a student could do just by random guessing. Suppose a student answers each question by picking one of the five...

Ann has taken a multiple-choice exam consisting of 25 questions. Each question has 5 choices of...

Ann has taken a multiple-choice exam consisting of 25 questions. Each question has 5 choices of which only one is the correct answer. Ann has correctly answered 9 questions. We would like to test if Ann is doing better than randomly guessing the answer to each question. Define the parameter to be tested. State the alternative hypothesis. _____________ Compute the test statistic. _____________ Compute the p-value. ____________ At the 1% level of significance, state your conclusion.

You take a quiz that consists of 5 multiple-choice questions. Each question has 5 possible answers,...

You take a quiz that consists of 5 multiple-choice questions. Each question has 5 possible answers, only one of which is correct. You will randomly guess the answer to each question. The random variable represents the number of correct answers. Construct the probability distribution for this random variable.

Suppose that you are taking a multiple choice test (consisting of only 4-answer-choice questions) for which...

Suppose that you are taking a multiple choice test (consisting of only 4-answer-choice questions) for which you have mastered 60% of the material. When you actually take the test, if you know the answer of a question, then you will answer it correctly for sure; if you do not know the answer, however, you can still guess the answer (meaning that you will have 25% chance of getting the correct answer). Finally, assume that your answer to each question is...

An exam has 8 multiple choice questions. Each question has 4 possible answers, only one of...

An exam has 8 multiple choice questions. Each question has 4 possible answers, only one of which is correct. If a student takes this exam and answers all questions at random, what is the probability that the student answers (a) only the first and the last question correctly? (b) only 2 questions correctly? (c) at least 2 questions correctly?

A quiz consists of 20 multiple choice questions, each with five possible answers, only one of...

A quiz consists of 20 multiple choice questions, each with five possible answers, only one of which is correct. If a student guesses on each question, what is the mean and standard deviation of the number of correct answers? Round to the nearest thousandth. ______________________________________________________________ A. The mean is 10. The standard deviation is 3.162. B.The mean is 4. The standard deviation is 1.789. C.The mean is 10. The standard deviation is 1.789. D.The mean is 4. The standard deviation...

Suppose a biology student is about to take an exam that is entirely multiple choice, where...

Suppose a biology student is about to take an exam that is entirely multiple choice, where each question has 5 answer choices. This student only studied 60% of the material that is covered on this exam, so let us assume that there is a 60% chance that she knows the correct answer to any given question. If she does not know the answer, she will choose an answer at random. a.If she answered a question on the exam correctly, what...

In a multiple choice exam, there are 7 questions and 4 choices for each question (a,...

In a multiple choice exam, there are 7 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (please round all answers to four decimal places) a) the first question she gets right is question number 3? b) she gets all of the questions right? c) she gets at least one question right?

Subjects