sta 117 final exam term 1, 2012.docx

FACULTY OF MANAGEMENT AND COMPUTING

BUSINESS MATHEMATICS STA 117

Term 1, 2012

12 May 2012

Time allowed: THREE HOURS

Total Number of pages: 13 Pages including the cover sheet

General Instructions: 1) This paper has TWO SECTIONS: Section A, and Section B

2) SECTION A: Answer ALL questions3) SECTION B: Answer ALL questions 4) Electronic, non-programmable calculators

maybe used.5) Read the question carefully before answering.6) Clearly write the question numbers and number

of sub-parts of the questions attempted.7) Your hand writing should be clear and legible.8) Answers without working may gain no credit.9) This paper carries 100 Marks.

SECTION ATHE EXAMINATION PAPER MUST BE COLLECTED IN WITH THE ANSWER SCRIPT

Final Exam: STA 117 2012/S1

Answer all questions

1. According to the Empirical Rule for normal distributions, approximately what percentage of the data must

fall within 2 standard deviations of the mean?

(A) 50%

(B) 68%

(C) 95%

(D) 99.7%

2. The number of tourists visiting the Maldives varies depending on the quarter of the year. This variation is

fairly predictable. That is, resort owners are aware of when to expect the highest or the lowest numbers of

tourists during the year. This is an example of:

(A) Seasonal variation

(B) Cyclical variation

(C) Secular trend

(D) Irregular variation

3. A qualitative variable that gives rise to exactly two possible outcomes is an example of:

(A) An ordinal variable

(B) A nominal variable

(C) A binary variable

(D) A quantitative variable

4. Which of the following techniques yields a simple random sample?

(A) Choosing volunteers from a business mathematics class.

(B) Grouping individuals by gender and choosing a proportion from each group.

(C) Numbering all the elements of a sampling frame and then using a random number table to pick cases

from the table.

(D) Randomly selecting schools, and then sampling everyone within the school.

5. Geometric mean of a set of values is given by Mean=n√ x1× x2× …× xn. The geometric mean of 25, 22,

18, 36 and 20 is:

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(A) 17.31

(B) 17.80

(C) 44.5

(D) None of the above

6. The simple interest earned on $45,000 deposited at a 8% p.a. for a period of 6 years 3 months is:

(A) $ 3,600.00

(B) $ 21,600.00

(C) $ 22,500.00

(D) $ 22,680.00

7. Which of the following variables is an example of a qualitative variable?

(A) Currency

(B) Number of children

(C) Shoe size

(D) Type of car

8. Which of the following is the possible strongest correlation?

(A) r=0.02

(B) r=−0.99

(C) r=+0.75

(D) r=+2.65

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The data in the following table is relevant to questions 9 to 11.The table shows weight distribution of 50 children.

Weight (in kg) No. of children

30-34 5

35-39 15

40-44 12

45-49 10

50-54 5

55-59 3

9. The mean weight of 50 children, in kilograms, to 1 decimal place is:

(A) 42.4

(B) 44.5

(C) 8.3

(D) 57.1

10. An estimate of the modal weight is:

(A) 46.54 kg

(B) 38.3 kg

(C) 40.5 kg

(D) 47.5 kg

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11. The lower class boundary of 35-39kg is:

(A) 35 kg

(B) 34.5 kg

(C) 39 kg

(D) 39.5kg

12. Given that mean marks of a group of students is 80 and standard deviation is 15. The coefficient of

variation, to the nearest whole number is:

(A) 19%

(B) 21%

(C) 5%

(D) 533%

13. Which of the following is TRUE for a positively skewed distribution?

(A) Mean > Median > Mode

(B) Mode > Mean > Median

(C) Mean < mode < Median

(D) Mean = median = mode

14. Index for a base period is always taken as:

(A) 100

(B) 200

(C) 50

(D) Zero

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15. Which of the following measures how far an observation typically is from the average as a percentage of the average?

(A) Coefficient of determination

(B) Coefficient of variation

(C) Standard deviation

(D) Inter-quartile range

16. A normal distribution has a mean of 75 and a standard deviation of 12. The z-score corresponding to an

observation of 82 is:

(A) 0.583

(B) 0.915

(C) 0.146

(D) -0.049

17. Long term decline or growth of a time series is known as:

(A) Secular trend

(B) Cyclical variation

(C) Irregular variation

(D) Seasonal variation

18. The measurements of spread or scatter of the individual points around the central point is called:

(A) Measure of central tendency

(B) Measure of dispersion

(C) Measure of skewness


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19. Which of the following is NOT a type of non-probability sampling?

(A) Quota sampling

(B) Systematic sampling

(C) Snowball sampling

(D) Convenient sampling

20. In financial mathematics, the amount of money borrowed or lend is called:

(A) The principal

(B) The accumulated amount

(C) The future value


END of Section A

[Total: 40 marks]

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SECTION B

Answer ALL questions

Question 1:

MCHE Bookstore has been selling the Believe It or Not: Wonders of Statistics Study Guide for 12

Semesters and would like to estimate the relationship between sales and number of sections of

elementary statistics taught in each semester. The following data have been collected.

Sales (units) 33 38 24 61 52 45

Number of sections 3 7 6 6 10 12

a) Calculate the regression line of number of sections on sales. (3 marks)

b) Interpret the slope of the regression line. (1 mark)

Question 2:

A firm’s marketing manager believes that the total sales for the firm next year can be modeled by

using a normal distribution, with a mean of $2.5 million and a standard deviation of $300,000.

a- What is the probability that the firm’s sales will exceed $3million? (2 marks)

b- What is the probability that the firm’s sales will fall within $150,000 of the expected level of

sales? (2 marks)

c- In order to cover fixed costs, the firm’s sales must exceed the break-even level of $1.8 million.

What is the probability that sales will exceed the break-even level? (2 marks)

Question 3:

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A company buys four types of raw materials. The prices (in £) and annual quantities used in the years

1999 and 2000 are given below:

Materials 1999 2000

1999 2000

Materials Price Quantity Price Quantity

A 50 90,000 90 80,000

B 60 10,000 50 20,000

C 60 1,000 50 2,000

D 50 25,000 60 20,000

(a) Calculate a simple (unweighted) aggregate price index for these materials in 2000, using 1999 as

the base year. (5 marks)

(b) Calculate an (unweighted) average of price relatives for 2000, using 1999 as the base year.

(5 marks)

(c) Calculate a (weighted) Laspeyres price index for 2000, using 1999 as the base year. (5 marks)

(d) Calculate a (weighted) Paasche price index for 2000, using 1999 as the base year. (5 marks)

(e) Account for the difference between the Laspeyres and Paasche indexes. (5 marks)

Question 4:

A saving scheme involves an initial investment of $1000 and an additional $50 at the end of each year

for the next 5 years. Calculate the receivable sum at the end of 5 years assuming that the annual rate of

interest paid is 8%. (5 marks)

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Question 5:

The number of new mortgage loans issued by a building society each quarter for three years is shown below:

Year Quarter Number of loans

1 1 32

2 46

3 50

4 26

2 1 362 483 504 30

3 1 382 483 524 34

(i) Calculate a centered four-point moving average trend. (5 marks)

(ii) Plot the original data on a graph and plot the moving average trend on the same graph.

(5 marks)

(iii) Calculate the seasonal variation estimates for each quarter. (5 marks)

(iv) Forecast the number of new mortgage loans for the four quarters of year 4. (5 marks)

END of Section B

[Total: 60 marks]

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Formula sheet

Laspeyre’s Index:∑ p t q0

∑ p0 q0

× 100

Paasche’s Index:∑ p t qt

∑ p0 qt

×100

Z-score: z=x−μ

σ

var=Sxx=∑ X2

n−[∑ X

n ]2

b=CovariancVar (x ) OR b=

Sxy

Sxx cov=Sxy=

∑ xy

n−∑ x∑ y

n × n a=

1n(∑ Y−b∑ X )

Laspeyre’s Index:∑ pn q0

∑ p0 q0

∗100

Paasche’s Index:∑ pn qn

∑ p0 qn

∗100

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Average of relative prices =sum of the simple price indexesk

=∑ ( pn

po

× 100)k

Price relative =pn

po

S=A 0 (1+ r100 )

t

+x (1+ r

100 )t

−x

r /100


Page | 12


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sta 117 final exam term 1, 2012.docx

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