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Chapter 5: Problem 32

One of the authors did a survey to determine the effect of students changing answers while taking a multiple-choice test on which there is only one correct answer for each question. Some students erase their initial choice and replace it with another. It turned out that \(61 \%\) of the changes were from incorrect answers to correct and that \(26 \%\) were from correct to incorrect. What percentage of changes were from incorrect to incorrect?

Short Answer

Expert verified
The percentage of changes from incorrect to incorrect were \(13 \% \)

Step by step solution

01

Understand the problem

The task at hand is to determine the remaining percentage of changes happening during a multiple-choice test. We know that 61% were changes from incorrect to correct answers and 26% were changes from correct to incorrect answers. But we don't know the percentage of changes from incorrect to incorrect, which we need to find out.
02

Add given percentages

First, add together the percentage changes given in the problem (i.e., \(61\% + 26\% \). The result of this calculation is \(87\%\). This represents the total known changes in answer.
03

Calculate the percentage of incorrect to incorrect changes

Now, to obtain the percentage of the changes from incorrect to incorrect answers, subtract the calculated percentage of total known changes from the total percentage which is always 100%. So, \( 100\% - 87\% = 13\%\).

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a. Explain how you could use a random number table to simulate rolling a fair six-sided die 20 times. Assume you wish to find the probability of rolling a 1 . Then report a line or two of the random number table (or numbers generated by a computer or calculator) and the values that were obtained from it. b. Report the empirical probability of rolling a 1 from part (a), and compare it with the theoretical probability of rolling a 1 .
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