**UNIVERSITY EXAMINATIONS: 2016/2017**

**EXAMINATION FOR THE CERTIFICATE IN BRIDGING **

**MATHEMATICS**

**MAT104 PROBABILITY AND STATISTICS**

**DATE: DECEMBER, 2016 TIME: 1 ½ HOURS**

**INSTRUCTIONS: Answer Question ONE and any TWO questions.**

**QUESTION ONE**

a) Explain the following terms:

i) Statistics (2 Marks)

ii) Probability (2 Marks)

ii) The price of a commodity increased by 15% between 2010 and 2012 but decreased by 8%

between 2012 and 2015. Using the price relative concepts or otherwise, determine the percentage

change in price between 2010 and 2015. (4 Marks)

iv) Consider the following data:

Using the data compute:

– The mean height (3 Marks)

– The standard deviation of these heights (5 Marks)

– The forth decile of the heights (4 Marks)

v) A dice is such that two of its faces are painted green and the rest yellow. The dice is used in a

game such that if you get a green face you win Ksh 50 while if you get a yello face you loose

Ksh 30. If the game is played by tossing the dice twice, find how much would one expect to win

in such a game. (5 Marks)

vi) The following table show the probability distribution of a random variable X:

Find:

– The probability of X being greater than zero (2 Marks)

– The mean of X (3 Marks)

**QUESTION TWO**

a) The following data relates to the cost of living in two major cities in Kenya:

Item Kisumu Mombasa Weight

Using the price relative concept determine the cost of living index taking Kisumu as the base city

and comment on the results. (10 Marks)

b) The following data was collected by CBM students on Kasarani road as they were doing some

field work on the different modes of transport along the highway:

Mode of transport No. Observed

Use a pie chart to represent the above information (10 Marks)

**QUESTION THREE**

a) Consider the following data

Class frequency

0- 9,999.9 4

10.000- 19,999.9 7

20,000- 29,999.9 5

30,000- 39,999.9 4

40,000- 49,999.9 3

50,000- 59,999.9 8

60,000- 69,999.9 3

70,000- 79,999.9 5

80,000- 89,999.9 3

90,000- 99,999.9 2

From the data compute:

i) The mean using coding method and taking 64,999.95 as the assumed mean. (5 Marks)

ii) The standard deviation using coding method and the same assumed mean in (i) above

(5 Marks)

iii) The sixth decile (5 Marks)

iv) The thirty second percentile (5 Marks)

**QUESTION FOUR**

The following table shows the performance of 80 students in a mathematics exam:

Marks No of students

1 – 10 3

11 – 20 5

21 – 30 5

31 – 40 9

41 – 50 11

51 – 60 15

61 – 70 14

71 – 80 8

81 – 90 6

91 – 100 4

Required:

i) Draw a cumulative frequency curve for the above data (10 Marks)

ii) Use the graph to estimate:

– The median (2 Marks)

– The inter-quartile range (2 Marks)

– The pass mark if 40 percent of the students were to be successful (2 Marks)

iii) Using computation estimate the position of a student who scored 63 points (4 Marks)

**QUESTION FIVE**

a) There are two baskets, basket A and basket B. Basket A contains 6 red beads while basket B

contains 8 yellow beads. Christine picks a basket at random and picks two beads at random one

after the other from the picked basket and hands them to her brother Ken.

i) Draw a probability tree diagram to represent this information (4 Marks)

ii) Find the probability that Ken receives:

– Two red beads (2 Marks)

– Two different color beads (2 Marks)

b) i) Define the term:

– Set (2 Marks)

– Overlapping of sets (2 Marks)

ii) A medical research group in a hospital is investigating the effectiveness of the three tests for a

certain disease, T1, T2 and T3. When 300 people with the disease were given the test, it was

found that:

– 54 reacted to all tests

– 147 reacted to T1

– 128 reacted to T2

– 182 reacted to T3

– 69 reacted to T1 and T2

– 75 reacted t0o T2 and T3

– 89 reacted to T1 and T3

Required:

i) Represent this information on a Venn diagram (4 Marks)

ii) How many people reacted to T3 only? (2 Marks)

iii) How many people reacted to none of these tests? (2 Marks)