Student Id No

STUDENT ID NO

MULTIMEDIA UNIVERSITY THIRD TRIMESTER FINAL EXAMINATION, 2005/2006 SESSION

PBS 0015–INTRODUCTION TO BUSINESS STATISTICS ( Foundation in Management Students Only )

22 MAY 2006 9.00 a.m.- 11.00 a.m. ( 2 Hours )

INSTRUCTIONS TO STUDENT 1. This question paper consists of 4 pages only excluding the cover page. 2. There are 3 questions in Section A and 2 questions in Section B. Answer ALL the questions in Section A and ONLY ONE question in Section B. 3. Please print all your answers for both sections A and B in the answer booklet provided. 4. All necessary workings MUST be shown. 5. Key Formulas are provided.

PBS0015

INTRODUCTION TO BUSINESS STATISTICS

22 MAY 2006

SECTION A – 60 marks (20 marks each) Answer all. Question 1 Consider the following probability density function:   3k x 3 , 0 x 4 f  x  , otherwise   0 where k is a constant.

a) b) c) d)

Determine the value of constant k. Find the mean and the variance of X. Find the cumulative distribution function, F (X ) . Use F (X ) in part (c) to evaluate P  0.2 X 3.8 .

(4 marks) (8 marks) (6 marks) (2 marks)

Question 2

A manager claims that a company has given the increment of salary for all the workers, an average of RM30.00 per month. A researcher wanted to check if this claim is true. A random sample of 35 employees taken by the researcher showed that these employees get the increment at an average of RM28.00 per month and a standard deviation of RM7.00. a)

Test at 2.5% significance level whether the average increment of all employees is less than RM30.00 per month or not. (10 marks)

b)

Test at 10% significance level whether the manager's claim is true or not. (10 marks)

Continued…

___________________________________________________________________________________________________________ HH/LA/NLN 1/6

PBS0015

INTRODUCTION TO BUSINESS STATISTICS

22 MAY 2006

Question 3

Raw material used in the production of a synthetic fiber is stored in a place which has no humidity control. Measurements of the relative humidity in the storage place and the moisture content of sample of the raw material (both in the percentages) on 12 days yielded the following results: Humidity (x)

42

35

50

43

48

62

31

36

44

39

55

48

Moisture Content (y)

12

8

14

9

11

16

7

9

12

10

13

11

a) b) c) d)

Find the least squares regression line yˆa bx . Give a brief interpretation of the value of b calculated in part (a). Predict the moisture content of the raw material when the humidity of the storage place is 40%. Compute the correlation coefficient r.

(12 marks) (2 marks) (2 marks) (4 marks)

Continued…

___________________________________________________________________________________________________________ HH/LA/NLN 2/6

PBS0015

INTRODUCTION TO BUSINESS STATISTICS

22 MAY 2006

SECTION B (20 marks) Please answer ONE question ONLY. Show the necessary workings. Question 1 (20 marks) a)

A farmer claims that 90% of the papayas he shipped out are ripe and ready to eat. Find the probabilities that among the 18 papayas shipped out, i) all 18 are ripe and ready to eat. (2 marks) ii) at least 14 are ripe and ready to eat. (2 marks) iii) 2 to 5 papayas are not ripe and not ready to eat. (3 marks) iv) calculate the mean, variance and standard deviation of the papayas that are shipped out are ripe and ready to eat. (3 marks)

b)

Lilliey Cakehouse determines on average, a demand for New York Cheese Cake are made 4 times a day. What is the probability that on a given day, this cake is i) requested more than 4 times. (2 marks) ii) not requested at all. (2 marks)

c)

The lifetime of a motorcycle is normally distributed with an average of 27 years and a standard deviation of 4.2 years. Find the probability that the lifetime of any given motorcycle is i) less than 20 years. (3 marks) ii) between 25 and 39 years. (3 marks)

Continued…

___________________________________________________________________________________________________________ HH/LA/NLN 3/6

PBS0015

INTRODUCTION TO BUSINESS STATISTICS

22 MAY 2006

Question 2 (20 marks)

a)

A sample of 38 expenses claimed by employees is randomly selected from a population that is normally distributed with the mean of RM120.00 and a standard deviation of RM25.00 i)

Find the mean and the standard deviation of the sample mean, x . (3 marks) Find the probability that the sample mean is less than RM110.00. (4 marks) Find the probability that the sample mean is between RM114.00 to RM125.00 (5 marks)

ii) iii)

b)

A department manager wants to know the mean amount spent by all customers at the store. The research officer of the department interviewed 40 customers and found that the mean amount spent by these customers at the store is RM80.00. It is known that the standard deviation of the amount spent by all customers is RM5.50. i)

What is the point estimate and the margin of error of the population mean,μ. (4 marks) Construct a 95% confidence interval for the mean amount spent by all customers at this store. (4 marks)

ii)

ANSWERS: SECTION A – 60 marks (20 marks each) Answer all. Question 1 a)

5 k 192

20 b) E ( X ) 2.8571  7 c)  0,  5 1 F ( X )  x 2 , 32  1,  d) 0.8791

80 E ( X 2 ) 8.8889  9

Var ( X ) 0.7259

x 0 0 x 4 x 4

___________________________________________________________________________________________________________ HH/LA/NLN 4/6

PBS0015

INTRODUCTION TO BUSINESS STATISTICS

22 MAY 2006

Question 2 a)

C = -1.96 Test Statistic z* = -1.69 we accept H0. Conclusion : The average increment of all employees is not less than RM30.00 per month. b) C1 = -1.65 and C 2 = 1.65 Test Statistic z* = -1.69 we reject H0. Conclusion : The manager's claim is not true.

Question 3 a) x 533 ,

x 44.4167

SS xx  854 .9167 b = 0.2690

y 132 , x

2

24529

xy 6093

y 11

SSxy  230 a 0.9481

Least square regression line, yˆa bx  yˆ0.9481 0.2690 x b) The value b 0.2690 means that, on average, the moisture content increases by 0.2690% for every 1% increase in the humidity. c)

d)

x 40% yˆ0.9481 0.2690 (40) 9.8119

y

2

1526

SS yy 74

r 0.9144

___________________________________________________________________________________________________________ HH/LA/NLN 5/6

PBS0015

INTRODUCTION TO BUSINESS STATISTICS

22 MAY 2006

SECTION B (20 marks) Please answer ONE questions ONLY. Show the necessary working. Question 1 (20 marks) a) i)

P(Y=0) = 0.1501

iii)

P (2 Y 5) 0.5433

iv) mean = 16.2

ii)

variance = 1.62

P ( X 4) = 0.3712

b) i)

ii)

P ( X 20) = 0.0475

c) i)

ii)

P ( X 14) = 0.9718

standard deviation = 1.27

P(X=0) = 0.0183 P(25 < X < 39) = 0.68228

Question 2 (20 marks) a) i)  x

= 120

x 4.0555 

ii) P( X <110) = 0.00676 

iii) P(114< X <125) = 0.8213 

b) x = 80 σ= 5.50

n=40 x 

 5 .5  n 40

= 0.8696

i) Point estimate of μ= RM80.00 Margin of error = 1.7044 ii) (78.30,81.70)

End Of Page ___________________________________________________________________________________________________________ HH/LA/NLN 6/6