QUESTION 1

Rachel set a class test for her students. The test is marked out of 100%. Her students' marks are summarized in the table below:

Marks (100%)	Number of students
15	1
23	1
35	2
46	4
51	5
55	15
61	25
64	13
67	1
72	3
75	12
78	6
86	1
93	1

(a) Construct an appropriate frequency table and draw a histogram to depict the data above [10 marks]

(b) Compute the mean [10 marks]

(c) Calculate the variance and standard deviation [10 marks]

(d) Calculate the coefficient of variation [5 marks]

(e) Interpret the distribution in your histogram [5 marks]

QUESTION 2

(a) A sample of test scores is obtained. The scores are displayed as follows:

12.9, 11.6, 13.5, 13.9, 12.1, 11.9, 13

Perform a test of hypothesis that the mean score is 12 at 5% significance level [10 marks].

(b) A chemical manufacturer is concerned about the degree of impurity in the raw material shipments purchased from a supplier. Taking a random sample of 10 shipments of raw materials, the standard deviation of impurity is 2.36. Find the 95% confidence interval for population variance [10 marks]