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Questions cover sampling from A-level results, continuous uniform modelling and probability calculations, expected values and hypothesis testing with a 5% significance level, and continuous distributions defined by piecewise probability density functions. It also includes modelling hit counts using suitable distributions, mean/variance computations, binomial and Poisson-based reasoning for blemished apples and trays, approximation methods, and assessment of model suitability using critical comments.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/statistics-2a-test-paper4/295670/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/statistics-2a-test-paper4/295670.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you choose a sampling unit and sampling frame for A-level results?","Question",{"text":112,"@type":113},"The question asks for suitable sampling units taken from final-year student A-level results and an appropriate sampling frame covering those students’ results in the Sixth Form College.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is a hypothesis test done when Phil gets 15 correct out of 30 at the 5% significance level?",{"text":117,"@type":113},"Compute the null distribution for the number correct when answers are random (selecting one of four options each time), then compare the observed result (15) to the critical region using a 5% significance level.",{"name":119,"@type":110,"acceptedAnswer":120},"What probability modelling methods are used for blemished apples and trays of 10 and boxes of 50 trays?",{"text":121,"@type":113},"Use binomial modelling for blemishes within a tray, then extend to tray-level events within a box. When selecting 20 trays and asking about more than 10 blemished apples, apply an appropriate approximation method to the relevant count distribution and account for the approximation’s adjustment.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},295670,1789721438,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":24},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","# STATISTICSA)UNIT 2\n\n1.A random sample is to betaken from the A-level results obtained by the final-year students ina Sixth Form College.Suggest(a)suitable sampling units,(1 mark)(b)a suitable sampling frame.(1 mark)(c)Would it be advisable simply to use the results ofall those doing A-level Maths?Explain your answer.(2 marks)  \n2.The random variable X,which can take any value in the interval 1≤X≤n,is modelled by thecontinuous uniform distribution with mean 12.  \n## (a)Show that n=23 and find the variance of X.(3 marks)\n\n(b)Find P(10\u003CX\u003C14).(2 marks)  \n3.The Driving Theory Test includes 30 questions which require one answer to be selected fromfour options.  \n(a)Phil ticks answers at random.Find how many of the 30 he should expect to get right.  \n## (2 marks)\n\n(b)If he gets 15 correct,decide whether this is evidence that he has actually done somerevision.Use a 5%significance level.(5marks)  \nAnother candidate,Sarah,has revised and has a 0-9 probability of getting each question right.  \n## (c)Determine the expected number of answers that Sarah will get right.(1 mark)\n\n(d)Find the probability that Sarah gets more than 25 corect answers out of 30.  \n(2 marks)  \n4.A continuous random variable Xhas probability density function  \nf(x)=0  \nx\u003C1,  \nf(x)=kx  \n1≤x≤4,  \nf(x)=0  \nx>4.  \n(a)Sketch a graph of f(x),and hence find the value ofk.  \n## (4 marks)\n\n(b)Calculate the mean and the variance of X.  \n## (6 marks)\n\nSTATISTICS 2(A)TEST PAPER4Page 2  \n   \n5.In World War II,the number of V2 missiles that landed on each square mile of London was,onaverage,3·5.Assuming that the hits were randomly distributed throughout London,  \n(a)suggest a suitable model for the number of hits on each square mile,giving a suitable valuefor any parameters.(1 mark)  \n(b)calculate the probability that a particular square mile received(i)no hits,(1 mark)(ii)more than 7 hits.(2 marks)  \n(c)State,with a reason,whether the model is likely to be accurate.(1 mark)In contrast,the number of bombs weighing more than 1 ton landing on each square mile was 45.  \n(d)Use a suitable approximation to find the probability that a randomly selected square milereceived more than 60 such bombs.Explain what adjustment must be made when using thisapproximation.(9marks)  \n6.In a fruit packing plant,apples are packed on to trays of 10,and then checked for blemishes.The chance of any particular apple having a blemish is 5%.If a tray is selected at random,find  \n(a)the probability that at least two of the apples in it are blemished,  \n(3marks)  \n(3 marks)  \n(b)the probability that exactly two are blemished.  \nTrays are now packed in boxes of 50 trays each.In one such box,find  \n(c)the probability that at most one tray contains at least two blemished apples,  \n(5 marks)  \n(d)the expected number of trays containing at least two blemished apples.  \n(2 marks)  \n(e)Use a suitable approximation to find the probability that in a random selection of 20 traysthere are more than 10 blemished apples.(3marks)  \n7.The time,in hours,taken to run the London marathon is modelled by a continuous randomvariable T with the probability density function  \n(a)Sketch the function f(t),and show that  \n(5 marks)  \n(b)Calculate the median value of T.  \n(9 marks)  \n(c)Make two critical comments about the model.  \n(2 marks)","cbCaisbWP3Y3ZCdw","https://ap.wps.com/l/cbCaisbWP3Y3ZCdw","pdf",453053,"English","# STATISTICS 2(A) TEST PAPER4\n## Sampling and probability models\n## Random variables with continuous uniform distribution\n## Multiple-choice answers and significance testing\n## Piecewise probability density function\n## World War II hit modelling and approximations\n## Blemished apples and tray box calculations\n## London marathon time distribution and median","[{\"question\":\"How do you choose a sampling unit and sampling frame for A-level results?\",\"answer\":\"The question asks for suitable sampling units taken from final-year student A-level results and an appropriate sampling frame covering those students’ results in the Sixth Form College.\"},{\"question\":\"How is a hypothesis test done when Phil gets 15 correct out of 30 at the 5% significance level?\",\"answer\":\"Compute the null distribution for the number correct when answers are random (selecting one of four options each time), then compare the observed result (15) to the critical region using a 5% significance level.\"},{\"question\":\"What probability modelling methods are used for blemished apples and trays of 10 and boxes of 50 trays?\",\"answer\":\"Use binomial modelling for blemishes within a tray, then extend to tray-level events within a box. When selecting 20 trays and asking about more than 10 blemished apples, apply an appropriate approximation method to the relevant count distribution and account for the approximation’s adjustment.\"}]","STATISTICS 2(A) TEST PAPER4 | PDF"]