關於2004 HKCEE Maths.的簡單問題

Tieria

2009-12-17 6:32 am

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※

回答 (1)

用戶9112

2009-12-17 6:46 am

✔ 最佳答案

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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