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Code No.: MTE 310S lndex No.:

Explain whether the events of the cars passingindependent or dependent events.

SECTIONA, '(50 marks)

I'Answer all questions in this section in the space provided.Thehavethree1154

(a)

Road Transport Department requires that all 1O-year old carsto undergo a performance test. The probabilities that1O-year old cars A, B and C wilf pass the performance test areIand - respectively.)

the test are(2 marks)

(b) From the information given, draw a tree diagram forperformance result of the cars A, B and C.(3

the teslmarks)

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Code No.: MTE 31 05Find the probability thatthe performancg test.

lndex No.:(i)c) only one of the three cars passes

(3 marks)

Calculate the probability that at most two out of the threecars will pass the performance test. emarks)

(ii)

Ur

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Code No.: MTE 31052' A machine manufactures 5000 ey{fidrical components in a five-hoursday, the mean value of the dial# treing O SOO cm with standarddeviation 0.30 mm.

(a) A random sample of 2s components is taken every 1s minutes.Determine the mean of thq sampting distribution or tn" meansand the standard sffs1,sf,'tfre means, correct to four significantfigures, for one day's ou-tput,from the machine, ii ine sampleswere takeni-(i) without replacement

(3 marks)

(ii) with replacement(2 marks)

e

sl

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-:qiqi-::.=ia.r

Code No.: MTE 3105 lndex No.:(b) Another sample of 50 cornponents is taken and the meandiameter is found to be 0.550 cm. Find the 95% confidenceinterval of the population mean. (2 marks)

(c) (i) Find also the 99% confidence interval of the populationmean for the sample in (b). (2 marks)

Compare:your answers in (b) and (cXi), what conclusioncan you make about them?(ii)

(1 rnark )

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Code No.: MTE 31Os lndex No.:elairns that the tr.ainees oflocal magazine has ru,n apublic intitutions watch less,local aver?Qe:is 25.4 hoursffihours,

*t4$Fn",tne general public, The&{&the standard deviation of 2(a) List the steps tor ,otU@r;k#eis-testing probtems.

"i

(4 marks)

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Code No.: MTE 3105

A sample qf 30a mean of 1'9(b)

lndex No,:

part in the survey and hasi:'listed in (a) , do, you haveat 'o = O.A1? (6 marks)

i

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Code No.: MTE 3105 lndex No.:

Age groupSummoned

50431 2A 10

You will use the chi-square test to test whether the number ofsummons are equally distributed ainong the age groups.(a) (i) What is 'Low Expected Values' in a chi-square test ?

a'

(1 mark)

(ii) What should you do if (a) happen?

(1 mark)

4. The traffic control department of a town wishes to determine whetherthe number of summons issued has a,n equal distribution among thetraffic offenders of various age groups. The following table displaysthe age group distribution for a sample of people summoned for trafficoffences.

{

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Code No.: MTE 3105 lndex No.:

(b) Test the claim that the distribution for each age groupsummoned is the same at q = 0^01 by using the followingsteps:(i) State the hypotheses to test the claim.

Ho:

Hr:

( ii) State the degree of freedomvalue.

(2 marks)

in the test and the critical

d.f.:

Critical Value:(2 marks)

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Code No.: MTE 31Os

-- -- l = ,,i

lndex No.:

(3 marks)

,* (iv) Wnte a conclusion of your test above.

(1 mark)

iL)

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6

Code No.: MTE 3105 lndexThe manager of Welcome Supermarket wants to know if there is adifference in the average time a customer has to wait in a check-outline in three different counters. Analysis of data collected on the check-out times (in minutes) for three counters is shown below:

Counter A Counter B Counter C4 5 13 8 36 .9 46 6 24 3 72 5 5

X,=+2' . =/

X, =6sl = 4.8

X. =3'67sl = 4'67

Grand Mean = 4.5556Grand variance = 4.4967

What hypotheses and claim will the Manager use in an ANOVAtest?

(2 marks)

o =0.01, test'the hypptheses in (a).State the degree of freedom for numerator anddenominator, hence find the critical value .

(numerator):(denominator):

,t

(a)

Ho.

Hr

(b) At(i)

df.df

.,.i:4{.,3.:.${4

,$..f4da,{

Critical Value(2 marks)

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f

'test,yalue.

Make a decision about the test above.

lndex No.:groups and the variance

(5 marks)

,fl(iii)

(1 mark)

i:

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Code No.: MTE 310S

SECTION B(50 marks)

Answer any two (2) questions in this section.1. A sample of 50 bulbs has the mean time to failure of gg5 hours.with thestandard deviation of 4g hour. construct a gg% confidence intervar forthe mean time to failure of the bulbs.(a) Explain how the confidence interval wiil be affected in thefollowing cases:

(i) A bigger sample of 500 rather than 5.0 was used.(ii) lt is given that the population of bulbs has standarddeviation of 45 hours

li

(12 marks)(b) lf the popuration of burbs has a mean time to fairure of g00 hoursand standard deviation of 45 hours, determine the probabirity thatthe mean time to failure of a random sampre of 36 burbs wiil be. between 890 hours and g15 hours. (5 marks)A production manager craimed that he is gs% confident that themean time to failure is between g52 to 94g hours, for any ,rrpt"taken from the.popuration, when o = 4s hours . show whether theclaim is truL *lin a sample rir" or 30 bulbs and the mean of gg2hours How large must a sample be selected if he wants to be3?r;r::;tident of the true mean differs from the sample mean by

\)

\r)

(8 rnarks)

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Code No.: MTE 3105

2. A construction company purchases steel cables from supprier X. Asample o'f 14 cables is selected, and the breaking strength (in kg) ofeach is found., The data is shown below." ,'907, 906, g0g, 906, g0g, 1000, g0g,i1001, 1002, g0g, 907, 905, g0g, g0g

Given that the breaking strength of the steel cables is normallydistributed with the population standard deviation being 30 kg,(a) Determine the mean and the standard deviation of the sample.The lot. of cables is rejected if the standard deviation of thesample is greater than 30 kg. At q = 0.01, should the lot berejected? (15 marks)

The construction company purchases more steel cables fromanother supplier Y. The standard deviation of the breakingstrength (in kg) for this population is 28 kg. A sample of 30cables is taken and it is found that the mean is 930 kg. At o =0.05, can it be concluded that there is no significant difference inthe breaking strength of the cables from the two suppliers?(10 marks)

(b)

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C.ode No.: MTE 3105

3. Explain hnro uses of the chi;sg14661g,,#t and the conditions required forthe use. (6 marks )

A study is ofing conduftd to determine whether there is arelationship between physical exercise and blood pressure' A randomsample of 2OO subjects is,,.se-lected, and they are classified intocategories as shown in the tab.le below. At s = 0 011 test the claim thatphysical exercise and blood pressure are not related.

Exercise Status Blood Ptessure

Exercise regularlyNo exercise

Low3015

Moderate5660

High2025

(19 marks)

v

1i

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Code No.: MTE 3105

(a).

(b)

Define"the line of best fit' in the regression analysis. (3 marks)Data from a sample of , 10 randomly selected students wascollected regardrng the number of hours they spent in a weekstudying f or final examination and their scores on thatexamination. The data was.as shown below.

Draw a scatter plot for the data.Determine the regression equation and use it to predict the scoreof a student who studies 12 hours per wee\.for the examination.

: (20 marks)Explain,rin your own words, the meaning of residual of points,and the slope in your regression equation obtained.

(3 marks)

@ Governnlent of Malaysia 2009 p7l

Hours :b I 5 I 11 5 10 6 15 4Score 60 76 45 80 85 65 82 50 90 45