Criteria for Assignment
- Analysis, graphical representation and summary of simple data set.
- Presenting financial data and making financial calculations.
- Calculate of simple probability models.
- Application of probabilistic reasoning.
- Use of tables to calculate Binomial and Poisson probabilities.
(Question 1) The following sample gives the valuation in £000's for 60 homes.
|
325
|
250
|
410
|
660
|
500
|
320
|
|
590
|
390
|
51
|
430
|
140
|
234
|
|
215
|
405
|
765
|
430
|
132
|
234
|
|
132
|
194
|
650
|
370
|
270
|
194
|
|
450
|
760
|
270
|
420
|
948
|
180
|
|
375
|
137
|
95
|
350
|
650
|
340
|
|
345
|
250
|
142
|
265
|
321
|
210
|
|
340
|
650
|
350
|
122
|
137
|
340
|
|
385
|
265
|
142
|
250
|
145
|
465
|
|
162
|
565
|
638
|
260
|
465
|
425
|
|
You are required to
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|
|
|
|
|
a) Create a box and whisker plot for the data (using graph paper).
b) Tabulate the data in the form of a grouped frequency distribution, using 9 equal- sized classes, having mid-points 100, 200, 300 etc.
c) Using the grouped data from part b):
(i) Estimate the mean and standard deviation.
(ii) Plot a cumulative relative frequency graph and estimate the median.
(iii) What is the modal class? How do the values of mean, median and midpoint of modal class compare? Does the standard deviation give a good idea of the variation in the data?(2) a) An investor in shares of various companies wishes to investigate how the companies, the market, the initial basket of shares and actual investments have performed over the past three years. The following table gives the company symbol (COMPANY), price per share (PRICE) and number of shares (HOLDING) of the investors share portfolio.
(Question 2) a) An investor in shares of various companies wishes to investigate how the companies, the market, the initial basket of shares and actual investments have performed over the past three years. The following table gives the company symbol (COMPANY), price per share (PRICE) and number of shares (HOLDING) of the investors share portfolio.
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COMPANY
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PRICE 2009
|
HOLDING
|
PRICE 2010
|
HOLDING
|
PRICE 2011
|
HOLDING
|
|
HSBC
|
608
|
500
|
632
|
600
|
511
|
500
|
|
BP
|
526
|
500
|
400
|
600
|
405
|
500
|
|
RBS
|
65
|
1000
|
48
|
800
|
24
|
600
|
|
BARC
|
367
|
400
|
623
|
800
|
152
|
600
|
|
HBOS
|
358
|
400
|
320
|
400
|
163
|
400
|
|
LLOY
|
110
|
800
|
74
|
1000
|
26
|
500
|
|
GSK
|
1195
|
400
|
1275
|
400
|
1270
|
400
|
|
AV
|
382
|
500
|
377
|
600
|
300
|
500
|
i. Calculate simple index number for each item in 2011, using 2009 as a base year and identify the best and worst company investment. [3]
ii. Calculate simple aggregate price index for 2010 and 2011, using 2009 as a base year, and comment on the results. [4]
iii. Calculate Laspeyres index number for 2010 and 2011, using 2009 as a base year, and comment on the results. [4]
iv. Calculate Paasche index number for 2010 and 2011, using 2009 as a base year, and comment on the results. [4]
b) Tryone Halls runs a stately home in Lancashire. Currently there is a small and old adventure area for children, that requires frequent maintenance. A proposal has been put forward to invest in a new adventure area which will attract new customers to visit the house and grounds. Three different proposals are being considered i) continuing with maintenance and keeping the play area as it is ii) modernizing the current area, and iii) creating a new expanded deluxe adventure area.
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Date
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Proposal I
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Proposal II
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Proposal III
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(Cost)
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(£10,000)
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(£100,000)
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(£350,000)
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Year 1 (Profit)
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2,000
|
24,000
|
80,000
|
|
Year 2 (Profit)
|
7,000
|
26,000
|
86,000
|
|
Year 3 (Profit)
|
5,000
|
28,000
|
95,000
|
|
Year 4 (Profit)
|
7,000
|
28,000
|
98,000
|
|
Year 5 (Profit)
|
6,000
|
30,000
|
98,000
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For the three alternatives based on the information in the table
i. Calculate the Payback Period, and decide on the preferred proposal. [3]
ii. Calculate the accountancy rate of return for the five years, and decide on the preferred proposal. [3]
iii. Calculate the Net Present Value given a discount rate of 4%, and decide on the preferred proposal. [6](3) A survey was made of 500 employees. The employees were categorized according to their salary: Band 1= £20,000 - £35,000, Band 2 = £35,000 - £45,000 and Band 3 = £45,000 - £65,000 and asked how they rated their job satisfaction. The following table was created.
(Question 3) A survey was made of 500 employees. The employees were categorized according to their salary: Band 1= £20,000 - £35,000, Band 2 = £35,000 - £45,000 and Band 3 = £45,000 - £65,000 and asked how they rated their job satisfaction. The following table was created.
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Job Satisfaction
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Salary
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Dissatisfied
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Moderately Satisfied
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Very Satisfied
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Total
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Band 1
|
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41
|
92
|
149
|
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Band 2
|
29
|
46
|
|
|
|
Band 3
|
|
|
74
|
|
|
Total
|
53
|
|
274
|
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a) Complete the table.[4]
b) Calculate the following probabilities for a person chosen at random from among the total sampled.
i. P(Very Satisfied)
ii. P(Band 1 and Moderately Satisfied)
iii. P(Band 3 or Very Satisfied)
iv. P(Dissatisfied | Band 1)
v. Are the events Band 2 and Moderately Satisfied independent? Explain your answer.
vi. Are the events Moderately Satisfied and Dissatisfied mutually exclusive? Explain your answer.
(Question 4) A salesperson for electricity solar panels knows from long experience that 9% of cold calls will result in a follow up interview being arranged. What is the probability that in a random sample of 50 calls:
a. Five interviews are arranged? [4]
b. At least two interviews are arranged? [2]
c. No more than eight interviews are arranged? [3]
d. Between 6 and 9 inclusive interviews arranged? [4]
(Question 5) Candidates for the graduate scheme of an oil major have to take two tests prior to interview, a psychometric test and an aptitude test. The results based on previous applicants show that P(Candidate passes psychometric test) = 0.8 and P(Candidate passes aptitude test) = 0.3.
Assume that performance on one test is independent of the other.
a) When a candidate applies for the post what is the probability he or she passes both test?
b) When a candidate applies for the post what is the probability that he or she passes just one of the two tests?
c) An ambitious, but incompetent candidate applies for the post repeatedly. What is the probability that he or she passes the psychometric test after 5 attempts?