STA 1104: PROBABILITY & STATISTICS I
QUESTION ONE (30 MARKS)
a) Distinguish between the following terms as used in Statistics
i.
Population and a sample
(2Marks)
ii.
A Histogram and a simple bar chart
(2Marks)
iii.
Measure of central tendency and measure of dispersion
(2Marks)
iv.
An event and a sample space
(2Marks)
v.
Independent and mutually exclusive events
(2Marks)
b) A sample of 20 First Year students reported their age as follows.
23
25
21
25
32
23
27
22
18
20
34
28
22
24
23
21
20
19
24
27
Compute the mean, median and mode of the age of the students (Do not group the
data)
(4Marks)
c) Giving an example in each case, distinguish between quantitative and qualitative data
(4Marks)
d) State the Bayes’ theorem
(2Marks)
e) Suppose a fair coin is tossed three times. What is the probability that the outcomes are
alike?
(4Marks)
f) Two events A and B are such that
and
i.
Find
(2Mark)
ii.
Find
(2Mark)
iii.
Are events A and B mutually exclusive? Justify your answer
(2Marks)
QUESTION TWO (20 MARKS)
a) The times taken by a group of people to solve a puzzle are shown below
Time(s) 10 – 14
Freq
1
i.
ii.
iii.
iv.
Calculate the;
mean
standard deviation
median
5th decile
15 – 19
3
20- 24 25- 29 30 – 34
7
10
15
35 – 39
12
(3Marks)
(3Marks)
(3Marks)
(3Marks)
b) A box contains 5 white balls and 4 black balls. Two balls are drawn from the box one
after the other without replacement.
i.
Present this problem using a tree diagram
(2Marks)
ii.
Find the probability that the balls taken are both white
(2Marks)
iii.
Find the probability that balls taken are both black
(2Marks)
iv.
Find the probability of drawing balls of different colours
(2Marks)
QUESTION THREE (20 MARKS)
a) The following table gives the distribution of the marks obtained by students in a test.
Marks
0-10
Frequency 4
10-20
20-30
30-40
40-50
50-60
60-70
70-80
10
16
22
20
18
8
2
Calculate the;
i.
Median
(3Marks)
ii.
Mean absolute deviation
(4Marks)
iii.
Quartile deviation
(5Marks)
b) A problem in Statistics is given to 3 students A, B and C whose chances of solving it
are
and
respectively. What is the probability that the problem would be
solved?
(4Marks)
c) The table below gives the birth rate and death rates of different countries during the
year 2007.
Country
Birth rate
Death rate
India
33
24
Germany
16
11
Irish Free State
20
14
Soviet Russia
40
18
New Zealand
18
8
Sweden
15
12
Construct a multiple-bar diagram for the data.
QUESTION FOUR (20 MARKS)
a) Consider the following data
(4Marks)
X
Freq
1
3
2
1
3
18
4 5
25 40
6
30
7
22
8
10
9
6
Use the assumed mean method to find the;
i.
Mean
(3Marks)
ii.
Standard deviation
(4Marks)
b) State two disadvantages of median as a measure of central tendency
(2Marks)
c) State one advantage and two disadvantages of diagrammatic presentation of data
(3Marks)
d) If
, and
, find;
i.
(2Marks)
ii.
(1Mark)
iii.
(3Marks)
iv.
Are the events A and B independent? Justify your answer
(2Marks)
QUESTION FIVE (20 MARKS)
a) The probability that A hits a target is
and the probability that B hits a target is .
They both fire at the target. Find the probability that;
i.
A does not hit the target
(1Mark)
ii.
Both hit the target
(1Mark)
iii.
One of them hits the target
(3Marks)
iv.
Neither hits the target.
(3Marks)
b) The following data shows the ages (in years) of 50 employees of a company
26
40
32
35
36
57
44
42
18
28
41
24
37
31
36
38
29
28
21
19
19
40
43
31
29
20
30
56
49
39
37
23
27
34
34
58
27
54
46
32
33
25
42
47
39
37
48
23
52
27
Construct a;
i. Frequency distribution table with class size of 5 starting with 18-22, 23-27,...
(4Marks)
ii.
iii.
Histogram, frequency polygon and frequency curve for the data (use the same
graph)
(5Marks)
Cumulative frequency curve for the data
(2Marks)
iv.
How many employees will have retired in 5 years time if the retirement age is
60 years?
(1Mark)