MBA604 Statistics Assignment 1
Part 1
1) (5 pts) An electronics company is about to launch a new product. If the serial number
for each piece produced has the following format: LLNNN where L stands for any
letter in the English alphabet and N is a number from 0 to 9, please answer the
following:
a) What is the name of the counting rule used to find all the possible outcomes?
b) How many different items can be uniquely numbered?
2) (5 pts) A company needs to select an expert group of consultants to provide advice
for a given project. How many possible selections consisting of 2 project managers, 2
legal advisors, 4 computer scientists and 3 systems engineers can be selected if the
company can pick from 4 project managers, 7 legal advisors, 5 computer scientists
and 6 systems engineers? Think carefully about the counting rules involved before
attempting to do any calculations.
3) (5 pts) Consider that you are a line manager in your current Corporation. There is a
0.50 probability that you will be promoted this year. There is a 0.65 probability that
you will get a promotion or a raise. The probability of getting a promotion and a raise
is 0.35. (Use letter P to denote promotion and letter R to denote raise.)
a. If you get a promotion, what is the probability that you will also get a raise?
b. What is the probability that you will get a raise?
Please show all the steps in your calculations
Part 2
Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two
cylinders are selected at random, what is the probability that
a. both defective cylinders are selected?
b. no defective cylinder is selected?
c. at least one defective cylinder is selected?
You are requested to solve the problem using two different approaches:
1. (9 pts) Solve the problem using your knowledge from the theory of probability
(chapter 4 in your e-text). If you wish to use letters in order to label the events:
Let "D1" denote the event of the first cylinder selected, to be defective.
Let "D2" denote the event of the second cylinder selected to be defective, when the
result (defective/non-defective) of drawing the first cylinder is unknown.
Therefore, P(D2) is the marginal/prior probability of the 2nd cylinder selected and
being defective, without knowing the selection result of the first cylinder. To reiterate,
P(D2) is a marginal/prior probability, not a conditional one.
If you find it helpful you can construct a tree diagram for this problem.
2. (9 pts) Solve the problem using your knowledge on probability distributions (chp 5 &
6). It is important to justify your choice of probability distribution to use. You will
need to decide whether your random variable is continuous or discrete and also need
to identify whether the sampling carried out is with or without replacement. These
steps will help you to identify the appropriate probability distribution to use.
3. (2 pts) Finally compare the two solutions. Elaborate on the computational complexity
of each one of them and the execution time when solving the problem by hand
(allowing the use of a basic scientific calculator but not statistical software).
• It is emphasised once more that in the first case you need to solve the problem
without using any known probability distribution formulas. You only need to use
your knowledge from chapter 4.
• You should get the same answer from the two methodologies that you use to solve the
problem. If there is a mismatch in your answers please go back and revisit the
problem before submitting.
• Please show all the steps in your calculations for both parts of the problem. Part 3
can be answered mainly through a short discussion.
Guidelines
Please read these guidelines very carefully.
Use of the template file
A template file “_MBA604_asn1.doc” has been provided. You are requested to write
your answers in this template file without removing or altering the headings that have
already been inserted. Please preserve the original fonts and formatting. You can insert as
many extra lines as you need, depending on how much space your solutions will take.
There is no need to include the assignment questions in the file that you will submit.
File-naming convention
The following file-naming convention must be used:
_MBA604_asn1.doc Please do not rename the template file. The submission module on
the VLE will automatically prepend your name when the file will be downloaded.
• Submit the document in “Microsoft Word 2003 format”, i.e. “.doc”. Unfortunately,
other file formats (e.g. docx, pdf, zip or other compressed files) cannot be accepted. If
you are using a later version of Microsoft office (2007 onwards), please make sure
that you save your file as .doc (Microsoft Word 2003 format).
Failure to comply with the above guidelines may result to loss of marks. If you are unsure
of any of the guidelines please ask before submitting.
Writing equations
If you don't want to use an equation editor for formulas, please follow the simple
approach below:
Please use the pipe character | for conditional probability and not a forward slash (/)
Please use the uppecase letter U for union
Please use the lowecase letter n for intersection