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關於2004 HKCEE Maths.的簡單問題
1. A large group of students sat in a Mathematics test consisting of two papers, Paper I and Paper II. The table below shows the mean, standard deviation and range of the test marks of these students in each paper: Test paperMeanMedianStandard deviationRangePaper I46.1... 顯示更多 1. A large group of students sat in a Mathematics test consisting of two papers, Paper I and Paper II. The table below shows the mean, standard deviation and range of the test marks of these students in each paper: Test paper Mean Median Standard deviation Range Paper I 46.1 marks 46 marks 15.2 marks 91 marks Paper II 60.3 marks 60 marks 11.6 marks 70 marks A student, John, scored 54 marks in Paper I and 66 marks in Paper II. (a) Assume that the marks in each paper of the Mathematics test are normally distributed. Relative to other students, did John perform better in Paper II than in Paper I? Explain your answer. (4 marks) Ans.: Paper I = (54 – 46.1) / 15.2 = 0.5197 Paper II = (66 – 60.3) / 11.6 = 0.4914 ※試解釋為何這樣計算※
最佳解答:
Paper I : The mean = 46.1 and standard deviation = 15.2 Consider Johns's score of 54, we can calculate the percentage of students who has score lower than this by calculating the z-score. z = (54 - 46.1) / 15.2 = 0.5917 The probability is Pr(z < 0.5917) Paper II : The mean = 60.3 and standard deviation = 11.6 Consider John's score of 66, we can calculate the percentage of students who has score lower than this by calculating the z-score. z = (66 - 60.3) / 11.6 = 0.4914 The probability is Pr(z < 0.4914) Comparing these calculations, since 0.5917 > 0.4914, the proportion of students who score less than John in Paper I is greater than the proportion of students who score less than John in Paper II. Hence the relative performance for John is better in Paper I than Paper II.
其他解答:
關於2004 HKCEE Maths.的簡單問題
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發問:1. A large group of students sat in a Mathematics test consisting of two papers, Paper I and Paper II. The table below shows the mean, standard deviation and range of the test marks of these students in each paper: Test paperMeanMedianStandard deviationRangePaper I46.1... 顯示更多 1. A large group of students sat in a Mathematics test consisting of two papers, Paper I and Paper II. The table below shows the mean, standard deviation and range of the test marks of these students in each paper: Test paper Mean Median Standard deviation Range Paper I 46.1 marks 46 marks 15.2 marks 91 marks Paper II 60.3 marks 60 marks 11.6 marks 70 marks A student, John, scored 54 marks in Paper I and 66 marks in Paper II. (a) Assume that the marks in each paper of the Mathematics test are normally distributed. Relative to other students, did John perform better in Paper II than in Paper I? Explain your answer. (4 marks) Ans.: Paper I = (54 – 46.1) / 15.2 = 0.5197 Paper II = (66 – 60.3) / 11.6 = 0.4914 ※試解釋為何這樣計算※
最佳解答:
Paper I : The mean = 46.1 and standard deviation = 15.2 Consider Johns's score of 54, we can calculate the percentage of students who has score lower than this by calculating the z-score. z = (54 - 46.1) / 15.2 = 0.5917 The probability is Pr(z < 0.5917) Paper II : The mean = 60.3 and standard deviation = 11.6 Consider John's score of 66, we can calculate the percentage of students who has score lower than this by calculating the z-score. z = (66 - 60.3) / 11.6 = 0.4914 The probability is Pr(z < 0.4914) Comparing these calculations, since 0.5917 > 0.4914, the proportion of students who score less than John in Paper I is greater than the proportion of students who score less than John in Paper II. Hence the relative performance for John is better in Paper I than Paper II.
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