Pearson Edexcel Level 3 GCE Mathematics Advanced PAPER 31 Statistics JUNE 2024 Combined Question Pa - Copy

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PAPER 31: Statistics
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Q:1/1/1/1/
*P72130A0120*

©2022lPearsonlEducationlLtd.

,1. Georgelthrowslalballlatlaltargetl15ltimes.
EachltimelGeorgelthrowslthelball,lthelprobabilityloflthelballlhittingltheltargetlisl0.48
ThelrandomlvariablelXlrepresentslthelnumberlofltimeslGeorgelhitsltheltargetlinl15lth
rows.
(a) Find

(i) P (Xl=l3)
(ii) P (Xlll5)
(3)
Georgelnowlthrowslthelballlatltheltargetl250ltimes.

(b) Uselalnormallapproximationltolcalculatelthelprobabilitylthatlhelwilllhitltheltargetlmor
elthanl110ltimes.
(3)
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*P72130A0220* 

,Questionl1lcontinued
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(TotallforlQuestionl1lisl6lmarks)
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 *P72130A0320* Turnloverl

, 2. Almanufacturerluseslalmachineltolmakelmetallrods.

Thellengthloflalmetallrod,lL cm,lislnormallyldistributedlwith
• almeanlofl8 cm

• alstandardldeviationloflx cm

Givenlthatlthelproportionloflmetallrodsllesslthanl7.902 cmlinllengthlisl2.5%l(a)ls
howlthatlxl=l0.05ltol2ldecimallplaces.
(2)

(b) Calculatelthelproportionloflmetallrodslthatlarelbetweenl7.94 cmlandl8.09 cmlinll
ength.
(1)
Thelcostloflproducinglalsinglelmetallrodlisl20p

Almetallrod
• wherelLl<l7.94lislsoldlforlscraplforl5p
• wherel7.94lllLlll8.09lislsoldlforl50p

• wherelLl>l8.09lislshortenedlforlanlextralcostlofl10plandlthenlsoldlforl50p

(c) Calculatelthelexpectedlprofitlperl500loflthelmetallrods.lGi
velyourlanswerltolthelnearestlpound.
(5)
Thelsamelmanufacturerlmakeslmetallhingeslinllargelbatches.

Thelhingesleachlhavelalprobabilitylofl0.015loflhavinglalfault.

Alrandomlsamplelofl200lhingeslisltakenlfromleachlbatchlandlthelbatchlislacceptedliflfewerl
thanl6lhingeslarelfaulty.
Thelmanufacturer'slaimlislforl95%loflbatchesltolbelaccepted.

(d)lExplainlwhetherlthelmanufacturerlisllikelyltolachievelitslaim.
(4)
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*P72130A0420* 