[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-394200-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-394200-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","math4510-statistics-review-exam-practice-questions","MATH4510 - Statistics Review - Exam Practice Questions","","Exam practice problems covering core statistics and probability topics: computing mean and standard deviation from a small set of scores; working with a probability density graph parameterized by k, including probabilities and solving for quantiles; comparing means and standard deviations when one additional observation is added to an existing sample. Additional tasks identify confidence intervals at different confidence levels, build relative frequency density histograms from grouped elevation data, compute probabilities and conditional/Bayes relationships, and apply normal-distribution assumptions for proportions, sample means, and z-tests.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/math4510-statistics-review-exam-practice-questions/394200/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/math4510-statistics-review-exam-practice-questions/394200.png","ImageObject",300,407,{"name":42,"@type":43},"Blitz","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-08","2026-09-26",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",14,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you compute the mean and standard deviation from the given exam scores?","Question",{"text":63,"@type":64},"Use the arithmetic mean for the central value, then compute the standard deviation from the deviations of each score from the mean (using the appropriate population/sample convention for the course). The problem then asks how many scores lie within one standard deviation of the mean.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find probabilities from the pdf graph in terms of k?",{"text":68,"@type":64},"Use the fact that the shaded/segmented areas separated by dashed lines correspond to given area expressions. Convert those areas into probabilities such as P(x\u003Cb) and P(x>a), then solve for r where P(x>r)=k by using cumulative area relationships.",{"name":70,"@type":61,"acceptedAnswer":71},"How does adding a 31st exam score equal to 82 affect the mean and standard deviation?",{"text":72,"@type":64},"The new mean depends on how the added score compares to the original mean: since it equals 82, it leads to the new mean being equal to the original mean. The standard deviation typically decreases or stays the same when the added observation matches the central tendency, and the problem requires qualitative justification.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},394200,1790936123,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":124,"preview_page_count":4},24464137899374,"https://us-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","1. Ten students got the following scores on an exam:  \n77 ; 77 ; 77 ; 82 ; 82 ; 82 ; 82 ; 89 ; 89 ; 94 :  \n(a) Find the mean of these scores.  \n(b) What is the standard deviation of these scores?  \n(c) How many scores fall within one standard deviation of the mean?  \n2. The following graph corresponds to the probability density function (pdf) for a random variable X . The regions separated by dashed lines have areas as shown. Here, k is a constant that is less than 1 .  \ny  \nx  \na b c  \n2(1-k)/5 2k/3  \n3(1-k)/5  \nk/3  \n(a) Find P (x \u003C b) (answer in terms of k) .  \n(b) Find P (x > a) (answer in terms of k) .  \n(c) Find r such that P (x > r) = k (answer in terms of a; b; c) .  \n(d) Looking at the above graph, about what do you think k is equal to? (Your answer should be an explicit real number.) Please explain.  \n3. The mean of a set of 30 exam scores is computed and found to equal 82 . (Not all scores are the same.) Later, a 31st exam is found. (It's a long story. It turns out the dog hadn't eaten that exam.) The exam is graded, and the score comes out also to be 82 .  \n(a) Is the mean of the new set of 31 scores less than, equal to, or greater than the mean of the original set of 30 scores? Please explain.  \n(b) Is the standard deviation of the new set of 31 scores less than, equal to, or greater than the standard deviation of the original original set of 30 scores? Please explain.  \n4. Given below are four intervals of real numbers.  \n(3:878 ; 3:922) ; (3:874 ; 3:926) ; (3:876 ; 3:920) ; (3:871 ; 3:929)  \nThree of them are con􀀌dence intervals for a population mean computed from the same sample, from some population X . One of these three is a 95% con􀀌dence interval, one a 98% con􀀌dence interval, and one a 99% con􀀌dence interval. The fourth interval is not a con􀀌dence interval computed from this sample. Which of the intervals is which? Please explain.  \n5. Colorado has 53 \\fourteeners,\" or mountains over 14,000 feet elevation (with at least 300 feet of prominence) . Below is a frequency table for the elevations of these 53 mountains.  \n\n| Elevation range (ft) | Frequency | Relative Frequency Density (RFD) |\n| --- | --- | --- |\n| [14000 ; 14100) | 23 |  |\n| [14100 ; 14200) | 9 |  |\n| [14200 ; 14300) | 14 |  |\n| [14300 ; 14400) | 4 |  |\n| [14400 ; 14500) | 3 |  |\n\n(a) Fill in the table above with RFD values. Include four decimal places.  \n(b) On the axes below, draw an RFD histogram for this data.  \n0:005 0:004 0:003 0:002  \n0:001  \nRFD  \nElevation (ft)  \n14 ;000 14 ; 100 14 ;200 14 ;300 14 ;400 14 ;500  \n(c) Given a randomly chosen fourteener, what is the probability that its elevation is at least  \n14,200 but less than 14,400 feet?  \n(d) If one of the 􀀌ve elevation ranges given in the above table is selected at random, what's the probability that fewer than 10 Colorado fourteeners have elevation within that range?  \n(e) Consider the following events:  \nE: A Colorado fourteener, chosen at random, has elevation in the range [14 ; 000 ; 14 ; 300) . F: A Colorado fourteener, chosen at random, has elevation in the range [14 ; 200 ; 14 ; 500) . Find the following values (it's OK to leave your answers as fractions):  \n􀀏 P (E)  \n􀀏 P (F )  \n􀀏 P (Fc ) (recall that Fc means the complement of F )  \n􀀏 P (Ej F )  \n􀀏 P (Ej Fc)  \n(f) Verify that Bayes' Law holds here for P (E) .  \n6. Suppose the radii X of ball bearings produced by a certain machine are normally distributed, with mean 􀀖 = 10 mm and standard deviation 􀀛 = 0:1 mm.  \n(a) Find the proportion of ball bearings produced by this machine that have radius between  \n9.8 mm and 10 .2 mm.  \n(b) Find the proportion that have radius greater than or equal to 10.2 mm. Hint: think about the symmetry of the standard normal curve about the mean.  \n(c) Find the number L such that 95% of the bearings have radius less than L standard deviations from the mean radius.  \n(d) If a random sample, of size n = 100, of ball bearings from this machine is chosen, what is the probability that the mean radius ","cbCaiaaY9eh5HQaO","https://ap.wps.com/l/cbCaiaaY9eh5HQaO","pdf",388019,"English","# Mean, standard deviation, and within-one-sigma counts\n# Probability density function (pdf) with parameter k\n# Updating mean and standard deviation after adding a score\n# Matching confidence intervals (95%, 98%, 99%)\n# Relative frequency density and histogram probabilities\n## Bin probabilities and Bayes' Law calculations\n# Normal distribution: proportions and sample-mean interval\n## Radius thresholds and two-sample summary comparisons\n# Sampling distributions of sample means (n=100)\n# Hypothesis testing for abnormal red blood cell volume (98%)\n# Confidence interval for a mean (98%)\n# Optimization and confidence interval/sample size for proportions","[{\"question\":\"How do you compute the mean and standard deviation from the given exam scores?\",\"answer\":\"Use the arithmetic mean for the central value, then compute the standard deviation from the deviations of each score from the mean (using the appropriate population/sample convention for the course). The problem then asks how many scores lie within one standard deviation of the mean.\"},{\"question\":\"How do you find probabilities from the pdf graph in terms of k?\",\"answer\":\"Use the fact that the shaded/segmented areas separated by dashed lines correspond to given area expressions. Convert those areas into probabilities such as P(x\\u003cb) and P(x\\u003ea), then solve for r where P(x\\u003er)=k by using cumulative area relationships.\"},{\"question\":\"How does adding a 31st exam score equal to 82 affect the mean and standard deviation?\",\"answer\":\"The new mean depends on how the added score compares to the original mean: since it equals 82, it leads to the new mean being equal to the original mean. The standard deviation typically decreases or stays the same when the added observation matches the central tendency, and the problem requires qualitative justification.\"}]","MATH4510 - Statistics Review - Exam Practice Questions | PDF",1790400007]