**UNIVERSITY EXAMINATIONS: 2015/2016**

**EXAMINATION FOR THE CERTIFICATE IN BRIDGING **

**MATHEMATICS**

**MAT104 STATISTICS & PROBABILITY**

**DATE: AUGUST 2016 TIME: 1½HOURS**

**INSTRUCTIONS: Answer Any THREE Questions.**

**QUESTION ONE**

a) Define the terms

i) Statistics (2 Marks)

ii) Probability distribution (2 Marks)

b) Consider the following data:

X 2 4 6 7 8 10

f 3 4 5 3 2 2

Compute:

i) The mean (3 Marks)

ii) The inter-quartile range (5 Marks)

iii) The 6th decile (3 Marks)

c) A bag contains 5 ripe mangoes and 6 unripe ones. John picks two mangoes at random one

after the other and gives it to his sister Esther only if it is ripe and if not returns it back into the

basket. Using a probability tree diagram, compute the probability that Esther gets at least one

ripe fruit.

2

(5 Marks)

d) The following frequency table gives the height in metres of some trees in a plantation:

class 1.5-

Frequency 6 10 18 12 10 4

i) Represent this information in cumulative frequency (ogive) curve (5 Marks)

ii) From the ogive curve estimate the boundary height if the trees are classified as 20% retarded,

50% standard and the rest overgrown

(3 Marks)

c) By calculation, find the position of a tree with a height of 5.7 metres (2 Marks)

**QUESTION TWO**

Consider the following data:

0 – 9,999

10,000 – 19,999

20,000 – 29,999

30,000 – 39,999

40,000 – 49,000

50,000 – 59,000

60,000 – 69,000

70,000 – 79,000

80,000 – 89,000

90,000 – 99,999

Required:

i) Compute the mean using 64,500 as an assumed mean (5 Marks)

3

ii) Compute the variance and standard deviation using 64,500 as an assumed mean(8 Marks)

iii) Compute the inter-quartile range (7 Marks)

**QUESTION THREE**

a) The price of a commodity increased by 35% between 2010 and 2014 but declined by 24%

between 2014 and 2015. Using the price relative concepts determine the percentage change in

the price of the commodity between 2010 and 2015.

(4 Marks)

b) The following table shows the monthly cost of living in two estates, estate A and B in Nairobi

in year 2015 and the significance/weight of each commodity:

Item Town A Cost (Shs) Town B Cost (Shs) Weight

Nancy is trying to establish where to reside at the lowest cost possible. Taking Town A as the

base town compute the composite/cost of living index and advise her accordingly.

(10 Marks)

c) A sample containing 10 values has a mean of 5 and a standard deviation of 3. Without

compotation explain what the standard deviation and the mean shall be if all the values are

multiplied by 3.

(2 Marks)

d) A discrete random variable X takes the following values with the corresponding probabilities:

x -30 -10 0 10 20 30

P(x) 0.1 K 0.15 K 0.1 0.25

Find:

i) The value of k (1 Mark)

ii) P(x˃0) (1 Mark)

iii) Mean of x (2 Marks)

**QUESTION FOUR**

a) Describe the following terms:

i) Probability (2 Marks)

ii) Mutually exclusive events (2 Marks)

iii) Set (2 Marks)

b) A fair six sided dice is painted Yellow on two of its faces and red on the remaining faces. A

game is played such that you win Ksh 50 if you get a yellow face and lose Ksh 30, if you get a

red dice. The dice is tossed five times. Let X represent the event yellow occurs:

i) Provide the probability distribution function of X and hence how much one would expect to

earn in this game

(12 Marks)

(II) The probability that one earns Ksh 200 (2 Marks)

**QUESTION FIVE**

The following data relates to the number of absent students at a school on monthly basis for 12

months of the year:

i) Compute the four point moving averages and centre them (8 Marks)

ii) Plot the time series data on a graph (5 Marks)

iii) Super-impose the line of best fit on the time series graph (5 Marks)

iv) Comment on the general trend of the data (2 Marks)