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?