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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Would you rather take a multiple-choice test or a

Chapter 3, Problem 168E

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QUESTION:

Problem 168E

Would you rather take a multiple-choice test or a full-recall test? If you have absolutely no knowledge of the test material, you will score zero on a full-recall test. However, if you are given 5 choices for each multiple-choice question, you have at least one chance in five of guessing each correct answer! Suppose that a multiple-choice exam contains 100 questions, each with 5 possible answers, and guess the answer to each of the questions.

a What is the expected value of the number Y of questions that will be correctly answered?

b Find the standard deviation of Y .

c Calculate the intervals μ ± 2σ and μ ± 3σ .

d If the results of the exam are curved so that 50 correct answers is a passing score, are you likely to receive a passing score? Explain.

                

Questions & Answers

QUESTION:

Problem 168E

Would you rather take a multiple-choice test or a full-recall test? If you have absolutely no knowledge of the test material, you will score zero on a full-recall test. However, if you are given 5 choices for each multiple-choice question, you have at least one chance in five of guessing each correct answer! Suppose that a multiple-choice exam contains 100 questions, each with 5 possible answers, and guess the answer to each of the questions.

a What is the expected value of the number Y of questions that will be correctly answered?

b Find the standard deviation of Y .

c Calculate the intervals μ ± 2σ and μ ± 3σ .

d If the results of the exam are curved so that 50 correct answers is a passing score, are you likely to receive a passing score? Explain.

                

ANSWER:

Solution:

Step 1 of 3:

A multiple -choice exam contains 100 questions, each with 5 possible answers.

We have at least one chance in five of guessing each correct answer.

We have to find

  1. The expected value of the number of Y of questions that will be correctly answered.
  2. The standard deviation of Y.
  3. The intervals and .
  4. If the result of the exam are curved so that 50 correct answers is a passing score, there is any chance to receive a passing score.

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