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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