KMKt AM025 (Student) PDF

Preview

Summary

ANSWER ALL QUESTIONS TIME: 2 HOURS SECTION A [25 marks]1. (a) If X ~ B  2,6 , find(i) Mean, variance and standard deviation. [6 marks]####### (ii) P ( X  2 ). [2 marks](b) If Y ~ P   3 , find(i) Mean and variance. [2 marks]####### (ii) P ( Y  3 ). [1 mark]####### (iii) P ( Y  2 ). [2 marks]2...

Description

Kolej Matrikulasi Kelantan

Session 2020/2021

ANSWER ALL QUESTIONS SECTION A [25 marks] 1.

TIME: 2 HOURS

(a) If X ~ B6, 0.2  , find (i) Mean, variance and standard deviation.

[6 marks]

P( X  2).

(ii)

[2 marks]

(b) If Y ~ P 3 , find (i) (ii)

Mean and variance.

(iii)

2.

[2 marks] [1 mark]

P(Y  3). P(Y  2).

[2 marks]

A Mathematics lecturer state that there is a linear relationship between the quiz marks (y) obtained by the students and the number of hours (x) spent on doing Mathematics exercises in a week. The summary of information for a sample of eight students is given below.

 x  68 ,  x

2

 620,

y

2

 6683,

 y  225 ,  xy  2032.

Find the linear regression equation yˆ  a  bx and explain the value of b. [6 marks]

3.

The selling price and quantity for several grocery items are given below. 2009

2010

Item

Price (RM/kg)

Quantity (kg)

Price (RM/kg)

Quantity (kg)

A

0.25

210

0.40

210

B

0.85

180

1.15

210

C

10.00

40

8.00

60

D

0.35

35

0.60

40

2009 : 100 Calculate and interpret. (a) The Laspeyres price index.

[3 marks]

(b) The Paasche quantity index.

[3 marks]

Kolej Matrikulasi Kelantan

Session 2020/2021

SECTION B [75 marks] 1.

2.

If Z ( x, y)  ln x 2  y 2 , show that

(a) Solve (4 x  4) e x  (b)

(c)

3

Evaluate



2

2 x3

[3 marks]

[3 marks]

(3  5x ) 5 dx.

0



7



7

Given that k ( x) d x  15 , k (x ) d x  11 and (i)

(ii)

[6 marks]

dx.

1

5

10

 k( x) d x  25. 1

 k( x)  2 d x.

[3 marks]

1

[3 marks]

10

Find

5

10





Find k( x) d x  k ( x) d x. 7

3.

 2 Z 2 Z   0. x 2 y 2

1

The Economy Travel Agency’s monthly revenue (RM’000) depends on the amount of money, x (RM’000) spent on advertising per month and the number of agents, y it employs in

accordance

with

the

2 2 following rule: R( x, y)  x  0.5 y  xy 8 x 3 y 20.

Determine the amount of money it should spend on advertising per month and the number of agents it should employ in order to maximize its monthly revenue. Hence, find the maximum revenue.

4.

Given

[11 marks]

S ( x)  x 2  10 x  20 and D ( x)  x 2  4 x  140 are supply and demand

functions, in RM. (a) Find the market equilibrium point.

[3 marks]

(b) Sketch the two functions and mark the region that represent the consumer’s surplus and the producer’s surplus. [3 marks] (c) Determine consumer’s surplus and producer’s surplus [6 marks]

Kolej Matrikulasi Kelantan 5.

Session 2020/2021

Company ZZZ produces three models of refrigerator Model AA, Model BB and Model CC. The selling price per unit and the number of units sold in the year 2017 and 2018 are given in the following table. Price (RM per unit)

Refrigerator

2017 800 1200 1500

Model AA Model BB Model CC

2018 850 1300 1600

Quantity (unit) 2017 150 450 180

2018 200 490 220

By using 2017 as the base year, calculate (a) the simple aggregate price index correct to three decimal places and interpret. [3 marks] (b) the simple average quantity index correct to three decimal places and interpret. [3 marks] (c) the Laspeyres quantity index and interpret. 6.

[3 marks]

A researcher wants to measure the relationship between the advertising expenditures and sales. The following table shows the data collected randomly from eight companies in a certain town. Advertising (RM’000)

Sales (RM’000)

3

70

4

120

3

110

5

100

6

140

5

120

4

100

5

130

(a) Calculate and interpret the Pearson’s correlation coefficient and the coefficient of determination. [7 marks] (b) Given that the linear regression equation is yˆ  46.666 14.762x . Estimate the sales if the company invests RM5300 in an advertising expenditure. [2 marks]

Kolej Matrikulasi Kelantan 7.

Session 2020/2021

One thousand students sat for a Statistics test. The marks obtained are normally distributed with mean 45 and standard deviation 9. (a) Find the probability that the students get more than 70 marks.

[3 marks]

(b) Find the probability that the students get less than 50 marks.

[3 marks]

(c) Find the probability that the students get between 50 and 75 marks.

[2 marks]

(d) If the passing mark is 55, estimate the number of students who pass the test. [4 marks] (e) If 70% of the students pass the test, obtain the minimum passing mark. State your answer to the nearest integer. [4 marks]

END OF QUESTION PAPER

Final Answer SECTION A

1.

(a) 1.2, 0.96,0.9798

0.2457( table), 0.2458(formula)

(b) 3, 3, 0.5768, 0.2241(table), 0.2240(formula) 2.

yˆ  3.9408  2.8452x For every 1hour sp ent on doing mathematics exercises in a week, the quiz mark increased 2.8452

3.

I  102.307 (The price increase by 2.307% compared to the base year) I  131.250 (Thequantityincrease by 31.25% compared to the base year)

(a) (b)

SECTION B 1. 2. 3. 4. 5.

6.

7.

x y ,Z y  2 ,Z Zx  2 2 x y x y2



2

2e x

 2 x 3







xx



y2  x2

x

2

 y2



2

, Z yy 

x2  y2

x

2

 y2



2

, Shown

 C ,  99508.5 , 31 , 10

RM 11000,14 number of agents, RM85,000 Market equilibriu m point is (5, 95) , CS  RM133.33 ,PS  RM208.33 (a) I  107.143 (b) I  121.481 (c) I  115.914 (a) r  0.7225 r 2  0. 5220 (b) RM124904.60 0. 00272 , 0. 7123 ,0. 28727 ,133, 41...