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A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answ multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what ca of the distribution of the variable number of answers changed from right to wrong? Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is 0.9 ✔ standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16% change fewer than 0 answers. Thus the distribution cannot ✔ be well approximated by a normal curve. There must be some values mor ✓ answers changed. This suggests that the distribution is positively: 1 standard deviation above the mean, that is, values above 1.9 How many standard deviations above the mean is three answers changed? 2.1 What can you say about the total number of students who changed at least three answers from correct to incorrect? (Round your answer down to number.)

A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answ multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what ca of the distribution of the variable number of answers changed from right to wrong? Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is 0.9 ✔ standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16% change fewer than 0 answers. Thus the distribution cannot ✔ be well approximated by a normal curve. There must be some values mor ✓ answers changed. This suggests that the distribution is positively: 1 standard deviation above the mean, that is, values above 1.9 How many standard deviations above the mean is three answers changed? 2.1 What can you say about the total number of students who changed at least three answers from correct to incorrect? (Round your answer down to number.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answer on a test containing 78 multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what can you tell about the shape of the distribution of the variable number of answers changed from right to wrong? of the students to Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is 0.9 standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16% change fewer than 0 answers. Thus the distribution cannot be well approximated by a normal curve. There must be some values more than answers changed. This suggests that the distribution is positively skewed 1 standard deviation above the mean, that is, values above 1.9 î How many standard deviations above the mean is three answers changed? 2.1 What can you say about the total number of students who changed least three answers from correct to incorrect? (Round your answer dow to the nearest whole number.) At most 1 X students changed at least three answers from correct to incorrect.
Transcribed Image Text:A paper reported that for a group of 76 college students, the average number of responses changed from the correct answer to an incorrect answer on a test containing 78 multiple-choice items was 0.9. The corresponding standard deviation was reported to be 1.0. Based on this mean and standard deviation, what can you tell about the shape of the distribution of the variable number of answers changed from right to wrong? of the students to Since the mean of the distribution is 0.9 answers changed and the standard deviation is 1.0 answers changed, 0 answers changed is 0.9 standard deviations below the mean. If the distribution were approximately normal, then we would expect about 16% change fewer than 0 answers. Thus the distribution cannot be well approximated by a normal curve. There must be some values more than answers changed. This suggests that the distribution is positively skewed 1 standard deviation above the mean, that is, values above 1.9 î How many standard deviations above the mean is three answers changed? 2.1 What can you say about the total number of students who changed least three answers from correct to incorrect? (Round your answer dow to the nearest whole number.) At most 1 X students changed at least three answers from correct to incorrect.
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### Analysis of Answer Changes in a Multiple-Choice Test In a study involving 76 college students, data revealed that the average number of responses changed from correct to incorrect on a 78-item multiple-choice test was 0.9. The standard deviation was recorded at 1.0. Based on this mean and standard deviation, we aim to understand the distribution shape of the variable number of answers changed from correct to incorrect. #### Distribution Analysis - **Mean and Standard Deviation Interpretation:** - Given the mean (μ) is 0.9 and the standard deviation (σ) is 1.0, a change of 0 answers is 0.9 standard deviations below the mean (0.9 - 0.9 = 0). - **Normal Distribution Assumption:** - If the distribution was normal, approximately 16% of students would change fewer than 0 answers. However, changing fewer than 0 answers is not logical, a hint that the distribution is not normal. - **Skewness of Distribution:** - Values exceeding one standard deviation above the mean are those above 1.9 answers changed (0.9 + 1.0 = 1.9). Given some students change more than 1.9 answers, this indicates the distribution is positively skewed. #### Standard Deviations From Mean - **Calculation for Three Answers Changed:** - To find how many standard deviations from the mean is three answers: \((3 - 0.9) / 1.0 = 2.1\). Thus, three answers changed is 2.1 standard deviations above the mean. #### Estimating Students Changing More Answers - **Students Changing at Least Three Answers:** - Considering the data, the number of students changing at least three answers from correct to incorrect is estimated to be at most 8 (rounded down to the nearest whole number). This analysis helps us understand student behavior regarding answer changes and the resultant distribution characteristics in academic assessments.
Transcribed Image Text:### Analysis of Answer Changes in a Multiple-Choice Test In a study involving 76 college students, data revealed that the average number of responses changed from correct to incorrect on a 78-item multiple-choice test was 0.9. The standard deviation was recorded at 1.0. Based on this mean and standard deviation, we aim to understand the distribution shape of the variable number of answers changed from correct to incorrect. #### Distribution Analysis - **Mean and Standard Deviation Interpretation:** - Given the mean (μ) is 0.9 and the standard deviation (σ) is 1.0, a change of 0 answers is 0.9 standard deviations below the mean (0.9 - 0.9 = 0). - **Normal Distribution Assumption:** - If the distribution was normal, approximately 16% of students would change fewer than 0 answers. However, changing fewer than 0 answers is not logical, a hint that the distribution is not normal. - **Skewness of Distribution:** - Values exceeding one standard deviation above the mean are those above 1.9 answers changed (0.9 + 1.0 = 1.9). Given some students change more than 1.9 answers, this indicates the distribution is positively skewed. #### Standard Deviations From Mean - **Calculation for Three Answers Changed:** - To find how many standard deviations from the mean is three answers: \((3 - 0.9) / 1.0 = 2.1\). Thus, three answers changed is 2.1 standard deviations above the mean. #### Estimating Students Changing More Answers - **Students Changing at Least Three Answers:** - Considering the data, the number of students changing at least three answers from correct to incorrect is estimated to be at most 8 (rounded down to the nearest whole number). This analysis helps us understand student behavior regarding answer changes and the resultant distribution characteristics in academic assessments.
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