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ASSIGNMENT 1ST SEMESTER : STATISTICAL ANALYSIS (STAT)
BUSINESS STATISTICS 1
(BS101)
STUDY UNITS COVERED
: CHAPTERS 1 - 8
DUE DATE
: 3:00 p.m. 15 MARCH 2011
TOTAL MARKS
: 100
INSTRUCTIONS TO CANDIDATES FOR COMPLETING AND SUBMITTING
ASSIGNMENTS
The complete ‘Instructions to Students for Completing and Submitting Assignments’ must be collected
from any IMM GSM office, the relevant Student Support Centre or can be downloaded from the IMM
GSM website. It is essential that the complete instructions be studied prior to commencing your
assignment. The following points highlight only a few important notes.
1. You are required to submit ONE assignment per subject.
2. The assignment will contribute 20% towards the final examination mark, and the other 80% will be
made up from the examination, however the examination papers will count out of 100%.
3. Although your assignment will contribute towards your final examination mark, you do not have to
earn credits for admission to the examinations; you are automatically accepted on registering for
the exam.
4. Number all the pages of your assignment (e.g. page 1 of 4) and write your name and surname,
student number and subject at the top of each page.
5. The IMM GSM requires assignments to be presented on plain A4 paper. You must show all
working calculations, including and where appropriate multiple choice working calculations.
6. A separate assignment cover, which is provided by the IMM GSM, must be attached to the front
cover of each assignment.
7. Retain a copy of each assignment before submitting, in case the original does not reach the IMM
GSM.
8. The assignment due date refers to the day up to which assignments will be accepted for marking
purposes. The deadline is 3:00 p.m. on 15 March 2011. Late assignments will be accepted, but 25
marks will be deducted from the maximum mark, if received after 3:00 p.m. on 15 March 2011
and up to 5:00 p.m. the following day, after which no assignments will be accepted.
9. If you fail to follow these instructions carefully, the IMM Graduate School of Marketing cannot
accept responsibility for the return of the assignment. It may even result in your assignment not
being marked.
Results will be available on the IMM GSM website, www.immgsm.ac.za, on Friday, 6 May 2011.
Assignment: 1st Semester 2011
© IMM Graduate School of Marketing
STAT/BS101
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SPECIFIC INSTRUCTIONS:
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Answer ALL the questions.
Read each question carefully to determine exactly what is required before
attempting the question.
Where applicable, formulae and computations must be shown, failing which,
marks will not be awarded.
Answers must be set out in a systematic way under appropriate headings
and sub-headings.
Number your answers clearly.
Graph paper is not required but graphs must be neat and according to scale.
Note: Presentation marks will NOT be awarded.
QUESTION 1
1.1
[10]
Consider the following frequency distribution:
Classes
10 – 14
15 – 19
20 – 24
25 - 29
Frequency
10
30
20
10
70
1.1.1 Calculate the class boundaries and class midpoints.
(2)
1.1.2 Construct a histogram from this frequency distribution. Graph paper is
not required but the graph must be neat and according to scale.
(3)
1.2
Consider the following frequency distribution:
Classes (in rand)
1.00 – 1.19
1.20 – 1.39
1.40 – 1.59
1.60 – 1.79
Frequency
2
6
9
3
20
1.2.1 Construct a cumulative less than frequency distribution.
(1)
1.2.2 Calculate the class boundaries and include them in the cumulative less
than frequency distribution.
(1)
1.2.3 Construct a cumulative less than ogive from the cumulative less than
frequency distribution. Graph paper is not required but the graph must
be neat and according to scale.
(3)
Assignment: 1st Semester 2011
© IMM Graduate School of Marketing
STAT/BS101
Page 3 of 4
QUESTION 2
[10]
Every 30 minutes a random sample of 5 items is drawn from the outgoing products
on a production line and tested. The data for the first 200 samples is shown below:
Number of defectives
in a sample of 5 items
Number of samples
0
1
2
3
4
5
74
65
30
16
10
5
2.1
Determine the sample mean, correct to two decimal places.
(3)
2.2
Determine the sample mode.
(2)
2.3
Determine the sample median and interpret your answer.
(3)
2.4
Based on the mean, the median and the mode, how is the distribution
skewed? Give a reason for your answer.
(2)
QUESTION 3
[10]
Consider the following 10 sample measurements:
0
2
0
1
5
2
5
2
0
15
3.1
Determine the value of the interquartile range.
(5)
3.2
Determine the standard deviation, correct to two decimal places.
(5)
QUESTION 4
[10]
A small business is about to receive an audit from the accounting firm it uses for
accounting purposes. Suppose that 5 percent of the invoices for the past quarter
contain errors. If the auditor randomly selects 20 invoices:
4.1
What is the probability that the auditor will find four invoices that contain
errors?
(4)
4.2
What is the probability that the auditor will find less than three invoices that
contain errors?
(4)
4.3
What is the expected number of invoices that contain errors? Show all
calculations correct to four decimal places.
(2)
QUESTION 5
[10]
The number of accidents per month in a large assembly plant is known to follow a
Poisson distribution with a mean rate of 4,5 per month.
5.1
What is the probability that there are eight accidents in a given month?
Assignment: 1st Semester 2011
(3)
© IMM Graduate School of Marketing
STAT/BS101
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5.2
What is the probability that there will be at least two accidents in a given
month?
(4)
5.3
What is the probability that there will be 12 accidents in four months? Show all
calculations correct to four decimal places.
(3)
ASSIGNMENT TOTAL: 50 x 2 = 100
Assignment: 1st Semester 2011
© IMM Graduate School of Marketing
STAT/BS101