DIT 072 INTRODUCTION TO PROBABILITY AND STATISTICS

 DIT 072 INTRODUCTION TO PROBABILITY AND STATISTICS

QUESTION ONE (24 MARKS)

a)    Define the following terms

                               i.            Statistics                                                                                          (2 marks)

                             ii.            Classical probability                                                                    (1 marks)

                          iii.            Conditional probability                                                             (1 marks)

b)    Name all the four stages that is involved in undertaking statistics. (4 marks)

c)     Construct frequency distribution table for the following marks obtained by 50 students.                                                                                                (7 marks)

57 67 46 30 44 56 43 54 65 57 41 50 48 51 62 59 58 55 48 47 34 27 60 52

65 36 68 72 54 51 23 50 38 42 63 75 12 33 26 39 35 47 43 52 56 59 64 77

15 21

d)    Compute the arithmetic mean, mode and median of the followings

3, 4, 1 , 1, 3, 2, 1, 5, 3, 4, 3                                                                       (4 marks)

e)    Suppose a game is to be played with a simple die assumed fair in this game a player wins $20 it a 2 turns up, $40 if 4 turns up, losses $30 if 6 turns up, will the player neither wins or loses if any other faces turned up                                                                                                               (3 marks)

f)      What is the expectation of a random variables.                            (2 marks)

QUESTION TWO (18 MARKS)

a)    Given the following data 3, 4, 5, 6, and 7 find the variance .     (2 marks)

b)    Construct a frequency histogram using 6 classes for this data.

76, 84, 76, 103, 92, 47, 98, 54, 80, 91, 69, 86, 83, 75, 93, 89, 96, 65, 94, 85

                                                                                                                        (6 marks)

c)     Given the distribution below find the variance.                            (6 marks)

x	10	15	16	20	17	14	10	16
f	3	6	7	11	9	5	4	2

 

d)    A group of accounting students are tested in QT techniques and management accounting. Their ranking in the two test were as follows                                                                                                                                 (4 marks)

QT	2	7	6	1	4	3	5	8
MA	3	6	4	2	5	1	8	7

Calculate the spearman rank correlation coefficient

 

QUESTION THREE (18 MARKS)

a)    Using the following data find the best line of feat.                       (6 marks)

 

Expenditure	25	30	15	75	40	65	24	35	70
Defective parts	50	35	60	15	46	20	45	42	22

 

b)    Find the arithmetic mean, mode and median of the following grouped frequency distribution.                                                                                 (12 marks)

class	frequency
10 - 19	7
20 - 29	15
30 – 39	18
40 – 49	25
50 – 59	30
60 – 69	20
70 – 79	16
80 – 89	7

 

 

QUESTION FOUR (18 MARKS)

a)    Define the following terms

Probability                                                                                                  (1 mark)

Range                                                                                                           (1 mark)

b)    A couple has two children what is the probability that both are boys given that at least one is a boy.                                                            (4 marks)

c)     Give the axioms of probability.                                               (3 marks)

d)    Find the variance of the following random variable                    (5 marks)

   f(x) = {1/2x   0                                 0 ≤ x ≤ 2

                                    otherwise

e)    When a coin is tossed the probability of having a head (H) is 1/3, if the coin is tossed 2 times what is the probability of having two tails (TT). Using a tree diagram                                                                                  (4 marks)

 

QUESTION FIVE (18 MARKS)

a)    The following table shows the pattern of inspection of expenditure and defective parts delivered to customers.                                     

Expenditure	25	30	15	75	40	65	24	35	70
Defective parts	50	35	60	15	46	20	45	42	22

Find how strong is the relationship between inspection in expenditure and defective and what extend they may predict the defective part deliveries from the knowledge of expenditure inspection. (8 marks)

b)    Find the standard deviation of the following grouped data    (10 marks)

 

Class	f
10 – 20	5
20 – 30	4
30 – 40	8
40 – 50	13
50 – 60	12
60 – 69	9
70 – 80	7
80 – 90	3