1. (a) Using the following sets:

A = {l,2,3,4,5,a,c}

B = {2,3,8,9, d}

C = {a, b,c,d}

Determine the following:

(i) AA(BUC);

(ii) BU(AAC);

(iii) B n C

(8 marks)

(b) The following distribution shows the number of customers who visited a hotel in a period of 42 days.

Number of customers Number of days

0 -4 4

4-8 12

8-12 8

12-16 7

16-20 5

20-24 6

(i) Present the data in a histogram.

(ii) Draw a frequency curve on the same graph in (i) above. (12 marks)

2. (a) The following data shows the marks scored by candidates in an interview for a secretarial post in an organisation:

20 50 80 40 85 40

40 70 60 70 40 50

30 30 45 50 20 60

(i) Prepare a frequency distribution table using the data above.

(ii) Using the result in (i) above, calculate:

(I) arithmetic mean;

(II) median.

(b) The following distribution shows the number of units of a product manufactured by a firm over a period of 36 months:

(i) Calculate the:

(I) arithmetic mean;

(II) standard deviation;

(III) mode;

(IV) Pearson’s Coefficient of Skewness.

(ii) Interpret the result in

(iv) above. (12 marks)

3. (a) The following data shows the number of customers served by a secretary of an organisation over a period of one week.

(i) Determine the regression equation in the form: y = a + bx.

(ii) Calculate the Coefficient of Determination.

(iii) Interpret the result in (ii) above. (12 marks)

(b) The probability that a customer will order for a cake in a restaurant is 0.4. On a certain day, 12 customers visited the restaurant. Calculate the probability that:

(i) 4 customers will order for a cake;

(ii) at most, 3 customers will order for a cake;

(iii) none of the customers will order for a cake.

4. (a) Explain four disadvantages of sampling in the collection of data. (8 marks)

(b) A manager of a game park claims that the average number of customers who visit the park per day is 24. The following data shows the number of customers who visited the park in a week:

6. (a) Explain each of the following types of matrices, using an example in each case:

(i) Transpose matrix;

(ii) Diagonal matrix;

(iii) Square matrix;

(iv) Scalar matrix.