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1.Listfourpropertiesofthestudent'sdistribution. [4Marks] 2.Mwangazalimiteddealsintheproductionofelectronicbulbs.Arandomsampleof10electronic bulbsproducedbythecompanyyieldedthefollowingresultsonthelifetimeofthebulbs. Lifetime(hours) 400 , 5 000 , 4 100 , 4 700 , 3 000 , 4 500 , 5 900 ,

1.Listfourpropertiesofthestudent'sdistribution.

[4Marks]

2.Mwangazalimiteddealsintheproductionofelectronicbulbs.Arandomsampleof10electronic

bulbsproducedbythecompanyyieldedthefollowingresultsonthelifetimeofthebulbs.

Lifetime(hours)

400

,

5

000

,

4

100

,

4

700

,

3

000

,

4

500

,

5

900

,

3

700

,

3

800

,

4

400

,

4

Required:

Testata%

5

percentlevelofsignificance,whetherthereisasignificantdifferencebetweenthe

samplemeanandthepopulationmean.

[6Marks]

3.Supposethatarandomsampleof100studentsisselectedtoestimatetheaverageamountoffees

arrears.ThesamplemeanisKsh.

000

,

54

withastandarddeviationofKsh.

000

,

25

.

Calculate:

(i)

A

%

95

confidenceintervalforthemean.[3Marks]

(ii)

Thesamplesizethatwouldberequiredtoestimatethemeantowithin

200

witha

%

95

confidencelevel.

[3Marks]

4.ThenumberoftaskssenttoanofficeprinterperminutefollowsaPoissondistributionwitha

parameter30.UsingthenormalapproximationtothePoissondistribution,findtheprobability

thatinoneminutetherearemorethan35tasks.

[4Marks]

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