**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