Ujian Pra Pentaksiran Prestasi STPM 2014 Semester 2

7/21/2019 Ujian Pra Pentaksiran Prestasi STPM 2014 Semester 2

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CONFIDENTIAL*

Section A[45 marks]

Answerallquestions in this section.

1 In a study of the use of mobile phones among students, a random sample of 11 students wasexamined for a particular week. he total length of calls made by 11 students were as follows.

1! "# #5 #$ 51 5# 54 55 $% !! 11%

&a' (ind the median and )uartiles for these data. [# marks]

&b' * +alue that is greater than ( )1## 5.1 QQQ + or smaller than ( )1#1 5.1 QQQ is defined asan outlier. how that 11% is the only outlier. [" marks]

&c' -sing a graph paper, draw the boxandwhisker plot showing all the information in parts &a'

and &b'. [# marks]

2 he table shows the probability of a discrete random +ariableX.

X % 1 " #

( )xXP = %." a b %."5

&a' /i+en that ( ) 55.1=XE , find the +alue of aand b. [4 marks]

&b' 0alculate ( )XVar . [# marks]

3 he random +ariableXis assumed to ha+e a probability density functionf, where

( )

= otherwise

xx

xf,%

$%,

1

1

&a' how that ( ) ( )""#$

1abbxaP = for $% ba . [4 marks]

&b' 0alculate the median ofX. [# marks]

4 * consumer association intends to study the relationship between rental rate of standard room and

ser+ice )uality of eight hotels in a city. he data obtained are shown in the table below.

2otel A B C D E F G H

3ental rate of a standardroom &3'

1% 1$% 1#% 15% "1% 14% 1% "5%

3anking by )uality # ! 5 4 $ 1 "

0alculate pearman6s rank correlation coefficient. 0omment on your answer. [5 marks]

STPM5%7# [Turn over

8his )uestion paper is 09:(I;


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CONFIDENTIAL*

he )uarterly sales and the centered mo+ing a+erage for a beauty product o+er the past three yearsare as follows>

?ear @uarter ales

&3 million'0entered mo+ing a+erage

1

1 #" "

# 1 #."5%

4 5 4.%%%

"

1 ! 4.5%%

" 4 5.!5

# # !.#!5

4 14 !.$"5

#

1 1% !.!5%

" # .5%%

# 5

4 1

&a' Alot the abo+e data as a time series. 0omment on the trend and seasonal components.[4 marks]

&b' -sing a multiplicati+e model, calculate the seasonal indices for the four )uarters. [4 marks]

&c' tate the )uarter which has the largest seasonal effect. [1 mark]

! he number of pensx&in thousand' produced by a factory and the total cost of production &in

thousand 3' for "% consecuti+e days are recorded. he results obtained ate summarised as

follows>

= %%.1!$x , = %%.4%% , %%.1!%"= x , %%.15%

"= , = "%.#!%%x .

&a' 0alculate the Aearson correlation coefficient between the number of pens produced and thetotal cost. Interpret your answer. [4 marks]

&b' (ind the e)uation of the least s)uares regression line of the total cost on the number of pens

produced. [# marks]&c'


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Section "[15 marks]

Answer anonequestion in this section.

# he number of luxury cars sold for each )uarter by a company and their coded )uartersxfor aduration of four years are shown in the table below.

Year Quarter Coded quarter $x% Number of cars $y%

"%%5

1 1 1%

" " 14

# # 11

4 4 "1

"%%$

1 5 11

" $ 1$

# ! 1%

4 ""

"%%!

1 14

" 1% 1

# 11 1#

4 1" ""

"%%

1 1# 1#

" 14 1$

# 15

4 1$ "5

&a' Alot the data as a time series. [# marks]

&b' 0omment on the pattern of the time series that you ha+e plotted in &a'. [1 mark]&c' -sing an additi+e model, find the adBusted seasonal +ariation for each of the four )uarters.

Crite down your answers correct to three decimal places. [5 marks]&d' 2ence, use the least s)uares method to fit a trend line to the seasonally adBusted time series

and predict the number of luxury cars sold for the fourth )uarter of "%%. [$ marks]

& r. an works fi+e days a week and he takes either a bus, a commuter or a taxi to his office. he

probability that he takes a taxi is %."% and the probability that he takes a commuter is %.5%. he

probabilities that he will arri+e late at his office if he takes a bus, a commuter, or a taxi are %.#%,%.1% and %.15 respecti+ely.

&a' (ind the probability that r. an will arri+e late at his office on any gi+en day. [# marks]&b' r. an arri+es late at his office on a gi+en day. determine the mode of transport that he is

likely to take. gi+e a reason for your answer. [4 marks]

&c' ;etermine the probability that in a gi+en week, r. an arri+es late at his office on alternate

days. [4 marks]&d' ;etermine whether the e+ents Dr. an arri+e late at his officeD and Dr. an take a bus to his

officeD are independent.


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END OF '(ESTIONS

STPM5%7# [Turn over

8his )uestion paper is 09:(I;

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Ujian Pra Pentaksiran Prestasi STPM 2014 Semester 2