Question

Alan has enrolled in two subjects and taken exams. Below are the lists of numbers showing class exam scores of two subjects. Alan’s scores are boldfaced:

Sociology: 85, 75, 62, 83, 90, 74, 77, 69, 70, 72

Psychology: 56, 60, 70, 59, 64, 62, 80, 66, 55, 79

a. Calculate the z-scores of Alan in the two subjects. Please show the calculation steps.

b. In which of the two subjects did Alan perform better relative to his classmates? In no more than four sentences, explain the basis of your answer.

c. Alan is also enrolled in another course on History. Its class mean exam score and standard deviation are 70 and 4.5 respectively. 74% of his classmates have a score lower than Alan. Based on these pieces of information and assuming that the exam scores in History are normally distributed, calculate Alan’s raw score in History.

Answer 1

(a)

(i)

Sociology :

From the given data, the following statistics are calculated:

n = 10

Mean = 757/10 = 75.7

SD= 8.3540

X = 77

So,

Z= (77 - 75.7)/8.3540 = 0.1556

(ii)

Psychology:

From the given data, the following statistics are calculated:

n = 10

Mean = 651/10 = 65.1

SD= 8.8122

X = 64

So,

Z= (64 - 65.1)/8.8122 = - 0.1249

(b)

In Sociology Alan performed better relative to his classmates because Z score for Sociology = 0.1556 > Z score for Psychology: = - 0.1249.

(c)

Mean = 70

SD = 4.5

74% of have lower score corresponds to area = 0.74 - 0.50 = 0.24 from mid value to RHS.

Table of Area Under Standard Normal Curve gives Z = 0.64

So,

Z = 0.64 = (X - 70)/4.5

So,

X = 70 + (0.64 X 4.5) = 72.88

So,

Answer is:

72.88