3.168 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 b What is the expected value of the number Y of questions that will be correctly answered? Find the standard deviation of Y. C Calculate the intervals 20 and μ ± 30. 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.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3.168
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
b
What is the expected value of the number Y of questions that will be correctly answered?
Find the standard deviation of Y.
C
Calculate the intervals
20 and μ ± 30.
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.
Transcribed Image Text:3.168 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 b What is the expected value of the number Y of questions that will be correctly answered? Find the standard deviation of Y. C Calculate the intervals 20 and μ ± 30. 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.
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