MAT104  PROBABILITY  STATISTICS  KCA Certificate Past Paper

UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE CERTIFICATE IN BRIDGING
MATHEMATICS
MAT104 PROBABILITY & STATISTICS
DATE: AUGUST, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.

QUESTION ONE [30 MARKS] – COMPULSORY
The table below shows the distribution of the wages in a week for 25 employees in a certain factory:

a) Using Ksh 11,499.5 per week as the assumed mean wage, compute:
i) The mean of the group’s wages (4 Marks)
ii) The standard deviation of the wages (6 Marks)
b) Estimate the median wage (5 Marks)
c) Estimate the earning of a person earning sh 10,500 if workers are ranked in ascending order of
earnings. (5 Marks)
d) A basket contains 7 ripe mangoes and 4 unripe ones. Two mangoes are picked randomly one at a time
and given to baby Natalie unless if unripe in which case is returned back into the basket:
i) Draw a probability tree diagram to represent this information (4 Marks)
ii) Find the probability that the two mangoes picked are ripe (3 Marks)
iii) The probability that at least one is ripe (3 Marks)
QUESTION TWO [20 MARKS]
a) A card is picked randomly from a pack of 52 playing cards. What is the probability that it is?
i) A Queen or Clover (3 Marks)
ii) A ten or Diamond (3 Marks)
b) The following data was collected by CBM students relating to the number of different motor vehicles
that passed through Thika road on a particular day:
Type of vehicle Number observed
Car 40
Lorries 20
Buses 10
Tuk tuks 15
Trailers 15
Use a bar chart to represent the above information (10 Marks)
c) 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 1,000 while if you get a yellow face you lose Ksh 400. If
the game is played by tossing the dice twice, find how much one would expect to earn in such a game
(4 Marks)
QUESTION THREE [20 MARKS]
a) The price of a commodity decreased by 15% between 2009 and 2014 but increased by 24% between
2014 and 2017. Using the price relative concepts determine the percentage change in the price of the
commodity between 2009 and 2017.
(4 Marks)
b) The following table shows the monthly cost of living in two estates, South A and South B in Eldoret in
year 2016 and the significance/weight of each commodity:

Washington Gathuki Mundu is trying to establish where to reside at the lowest cost possible. Taking
South A as the base estate, compute the composite/cost of living index and advise him accordingly.
(10 Marks)
c) A discrete random variable X takes the following values with the corresponding probabilities:

Find:
i) The value of k (2 Mark)
ii) P(x˃0) (2 Mark)
iii) Mean of x (2 Marks)
QUESTION FOUR [20 MARKS]
The data below reflects the measurements of wheat production produced in different factoties in the Rift
Valley province
Weight No of times produced
0 9999.5 5
10,000 – 19,999.5 6
20,000 – 29,999.5 4
30,000- 39,999.5 7
40,000 – 49,999.5 5
50,000 – 59,999.5 6
60,000 – 69,999.5 4
70,000 – 79,999.5 3
Compute:
i) The mean using coding method and 64,999.75 as the assumed mean (5 Marks)
ii) The standard deviation using coding and 64,999.75 as the assumed mean (5 Marks)
iii) Compute the mode of the data (5 Marks)
iv) Compute the median of the data (5 Marks)
QUESTION FIVE [20 MARKS]
a) A couple has 0.39 chance of getting a baby boy at Any one delivery. The couple intends to have FOUR
children. Let X represent the possible number of boys at any one delivery.
i) Generate the probability distribution table of X (6 Marks)
ii) Hence the expected number of boys in this family. (4 Marks)
iii) What is the probability of having at least 2 boys? (2 Marks)
b) A biased coin is such that the on any toss, getting a tail is thrice as likely as getting a head. If the coin
is tossed 10 times, find the probability that:
i) Exactly four heads appear (2 Marks)
ii) Exactly six heads appear (2 Marks)
iii) At least two heads appear (4 Marks

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