Reference no: EM132710414
QUESTION ONE
a) An examination has a mean mark of 60.7 and a standard deviation of 12.3.You may assume the marks follow a Normal distribution.
i) A candidate needs a mark at least 40 to pass .What percentage of candidates fail?
ii) The board a wards distinctions to the best 10% of the candidates. What is the lowest mark a candidate will need to gain a distinction?
iii) The list of passing candidates is published the day before the list of distinctions .What is the probability that a candidate who has passed will have a distinction?
b) An airline does a survey of the weights of adult passengers travelling on its flights. It finds that 5% weigh more than 84.3kg and 2% weigh less than57.2kg. Assuming that the weights of adult passengers on its flights are normally distributed, find the mean and standard deviation of the weights.
QUESTION TWO
a) The ranking of 10 students in two subjects is given below
|
Student
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
English
|
3
|
5
|
8
|
4
|
7
|
10
|
3
|
3
|
6
|
9
|
|
Kiswahili
|
6
|
4
|
9
|
4
|
4
|
4
|
10
|
5
|
7
|
6
|
Use rank correlation coefficient to determine the rank correlation coefficient between the two subjects and comment on your results.
b) State the merits and demerits of rank correlation
QUESTION THREE
The following table shows yields of a certain crop in grams.
|
Yields (g)
|
40-49
|
50-59
|
60-69
|
70-79
|
80-89
|
90-99
|
100-109
|
|
Frequency
|
3
|
7
|
25
|
17
|
15
|
11
|
2
|
Use it to calculate the;
i) Median
ii) Mode
iii) The geometric mean,
iv) The harmonic mean,
v) The standard deviation
QUESTION FOUR
a) State the twobasic statistical laws upon which the sampling techniques depends.
b) Define the term hypothesis testing and explain the procedure generally followed in testing hypothesis
c) An environmental researcher wishes to test a new organic fertilizer to find if it has an effect on maize yield. Give your possible hypothesis and explain the terms; two tailed and one tailed using the above example.
d) Explain using the above example type I and type II errors and state which one is preferable and why.
QUESTION FIVE
a) Define a statistical sample and give two basic statistical laws which sampling technique depends.
b) List the properties of a normal distribution.
c) Write detailed notes on each of the following
i) Data collection
ii) Design of a good questionnaire