Example of normal distribution, Mathematics

The mathematics results of 20 first-year university students are given, together with their results of their performances in the year 12 semester Test and Final Assignment:

Year 12

Year 12

First Year University

Assignment Result

Final Test Result

Mathematics Results

54

54

57

66

62

61

62

65

73

58

64

74

67

67

82

58

68

80

66

68

78

68

68

74

57

68

63

63

69

75

72

70

92

69

71

90

67

73

73

72

75

82

77

74

90

75

73

91

61

72

93

68

77

94

73

82

100

97

83

82


a) Which of the two Year 12 Assessment items are more closely related to performance in Mathematics at First Year University? Justify your answer briefly.

b) Standardise and combine the two Year 12 results and find the z- scores for this total for each student. How closely does these totalled scores relate to University performance? Is it better or worse than the individual item results? Justify your answer briefly.

c) Which of the four sets of data (forth set of data, is the answer of b) used most closely fits a normal distribution? Justify your answer briefly.

d) From the set selected in (c), use your information to determine between what scores you would expect to find 70% of the distribution. (Show full working, each step).

From the same set, between what scores would you find a spread of 1.5 standard deviations?

Posted Date: 3/19/2013 5:14:30 AM | Location : United States







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