a) Differentiate the following terms as used in statistics. i. Independent events and mutually…

a) Differentiate the following terms as used in statistics.

i. Independent events and mutually exclusive events [2 Marks]ii. Continuous variables and discrete variables [2 Marks]

b) The Marks obtained by 30 students in a mathematics test marked out of 20 are as shown below

Marks	8	9	10	11	12	14	15	17	18	20
No. of students	2	3	4	4	5	3	3	3	2	1

Compute.

i. The mode

ii. Median

iii. Mean

iv. Standard deviation [8 Marks]

c) The first of the two groups has 100 items with mean 45 and variance 49. If the combined group has 250 items with mean 51 and variance 130. Find the mean and standard deviation of the second group.[5 Marks]

d) The following data refers to examination Marks versus hours of study per week of a sample of eight candidates that sat for business statistics examination in 2010.

Exam mark(Y)	64	61	84	70	88	92	72	72
Hours of study(X)	20	16	34	23	27	32	18	22

Calculate:

i. The Pearson’s product moment of correlation [5 Marks]

ii. The coefficient of determination between examination Marks and hours of study.

[2 Marks]

e) If 50% of families subscribe to the morning paper, 65%of the families subscribe to the afternoon paper and 85% of these families subscribe to at least one of the two newspapers, what proportion of the families subscribe to both newspapers. [3 Marks]

f) Under what condition does P(A/ B) ?P(A)? [1 Mark]

g) What is the addition rule of probability and for what type of events is it valid?