[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-294320-105":59,"doc-detail-294320-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","practice-problems-for-biostatistics-describing-data-the-normal-distribution","Practice Problems for Biostatistics - Describing Data, the Normal Distribution","","A set of biostatistics practice problems focusing on descriptive statistics and key properties of the normal distribution. Topics include computing sample mean, median, and standard deviation, assessing how summary measures change after altering observations, and using normality assumptions to interpret standard deviations and percentages. Additional questions address confidence intervals and sampling distributions, including effects of sample size on standard error and interval width.",{"@graph":69,"@context":123},[70,84,106],{"@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/practice-problems-for-biostatistics-describing-data-the-normal-distribution/294320/",{"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/practice-problems-for-biostatistics-describing-data-the-normal-distribution/294320.png","ImageObject",300,407,{"name":92,"@type":93},"Anda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you compute the sample mean, median, and standard deviation from the given incubation-period data?","Question",{"text":113,"@type":114},"Calculate the mean as the arithmetic average, the median as the middle value after ordering, and the standard deviation using the sample formula based on deviations from the mean.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"If an observation (6.3) is changed to 1.5, what happens to the sample mean, median, and standard deviation?",{"text":118,"@type":114},"Changing a value to 1.5 shifts the center and reduces or increases spread depending on how far the new value lies from the existing mean and how it affects the ordered median position.",{"name":120,"@type":111,"acceptedAnswer":121},"How does increasing sample size affect confidence intervals and standard error?",{"text":122,"@type":114},"For mean confidence intervals, larger sample size generally produces a smaller standard error, so the interval becomes narrower. The problems ask this directly by comparing cases like using 200 vs. 100 observations.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},294320,1789682359,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":31},962075006959,"https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297","PRACTICE PROBLEMS FOR BIOSTATISTICS  \nBIOSTATISTICS  \nDESCRIBING DATA, THE NORMAL DISTRIBUTION  \n1. The duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period. The incubation periods of a random sample of 7 HIV infected individuals is given below (in years):  \n12.0 10.5  \n9.5 6.3  \n13.5 12.5  \n7.2  \na. Calculate the sample mean.  \nb. Calculate the sample median.  \nc. Calculate the sample standard deviation.  \nd. If the number 6.3 above were changed to 1.5, what would happen to the sample mean, median, and standard deviation? State whether each would increase, decrease, or remain the same.  \ne. Suppose instead of 7 individuals, we had 14 individuals. (we added 7 more randomly selected observations to the original 7)  \n12.0 10.5 5.2  \n9.5 6.3 13.1  \n13.5 12.5 10.7  \n7.2 14.9 6.5  \n8.1 7.9  \nMake an educated guess of whether the sample mean and sample standard deviation for the 14 observations would increase, decrease, or remain roughly the same compared to your answer in part (c) based on only 7 observations. Now actually calculate the sample mean standard deviation to see if you were right. How does your calculation compare to your educated guess? Why do you think this is?  \n2. In a random survey of 3,015 boys age 11, the average height was 146 cm, and the standard deviation (SD) was 8 cm. A histogram suggested the heights were approximately normally distributed. Fill in the blanks.  \na. One boy was 170 cm tall. He was above average by   SDs.  \nb. Another boy was 148 cm tall. He was above average by   SDs.  \nc. A third boy was 1.5 SDs below the average height. He was   cm tall.  \nd. If a boy was within 2.25 SDs of average height, the shortest he could have been is   cm and the tallest is   cm.  \ne. Here are the heights of four boys: 150 cm, 130 cm, 165 cm, 140 cm. Which description from the list below best fits each of the boys (a description can be used more than once)? Justify you answer  \n– Unusually short.  \n– About average.  \n– Unusually tall.  \n3. Assume blood-glucose levels in a population of adult women are normally distributed with mean 90 mg/dL and standard deviation 38 mg/dL.  \na. Suppose the “abnormal range” were defined to be glucose levels outside of 1 standard deviation of the mean (i.e., either at least 1 standard deviation above the mean, or at least 1 standard deviation below mean) . Individuals with abnormal levels will be retested. What percentage of individuals would be called “abnormal” and need to be retested? What is the normal range of glucose levels in units of mg/dL?  \nb. Suppose the abnormal range were defined to be glucose levels outside of 2 standard deviations ofthe mean. What percentage of individuals would now be called“abnormal”? What is the normal range of glucose levels (mg/dL)?  \n4. A sample of 5 body weights (in pounds) is as follows: 116, 168, 124, 132, 110. The sample median is:  \na. 124.  \nb. 116.  \nc. 132.  \nd. 130.  \ne. None of the above.  \n5. Suppose a random sample of 100 12-year-old boys were chosen and the heights of these 100 boys recorded. The sample mean height is 64 inches, and the sample standard deviation is 5 inches. You may assume heights of 12-year-old boys are normally distributed. Which interval below includes approximately 95% of the heights of 12-year-old boys?  \na. 63 to 65 inches.  \nb. 39 to 89 inches.  \nc. 54 to 74 inches.  \nd. 59 to 69 inches.  \ne. Cannot be determined from the information given.  \nf. Can be determined from the information given, but none of the above choices is correct.  \n6. Cholesterol levels are measured on a random sample of 1,000 persons, and the sample standard deviation is calculated. Suppose a second survey were repeated in the same population, but the sample size tripled to 3,000. Then which of the following is true?  \na. The new sample standard deviation would tend to be smaller than the first and approximately about one-third the size.  \nb. The new sample standard deviation would tend to b","cbCaicr50bLuHcGn","https://ap.wps.com/l/cbCaicr50bLuHcGn","pdf",187039,"English","# Describing Data, the Normal Distribution\n## Incubation periods and sample statistics\n## Height survey and normal-distribution intervals\n## Blood-glucose abnormal ranges\n## Sample median and interval estimates\n## Sample standard deviation across surveys\n# Sampling Distributions, Confidence Intervals\n## Standard error and variability by sample size\n## Confidence intervals for mean blood pressure\n## Sampling distribution shape after skewed relapse times","[{\"question\":\"How do you compute the sample mean, median, and standard deviation from the given incubation-period data?\",\"answer\":\"Calculate the mean as the arithmetic average, the median as the middle value after ordering, and the standard deviation using the sample formula based on deviations from the mean.\"},{\"question\":\"If an observation (6.3) is changed to 1.5, what happens to the sample mean, median, and standard deviation?\",\"answer\":\"Changing a value to 1.5 shifts the center and reduces or increases spread depending on how far the new value lies from the existing mean and how it affects the ordered median position.\"},{\"question\":\"How does increasing sample size affect confidence intervals and standard error?\",\"answer\":\"For mean confidence intervals, larger sample size generally produces a smaller standard error, so the interval becomes narrower. The problems ask this directly by comparing cases like using 200 vs. 100 observations.\"}]","Practice Problems for Biostatistics - Describing Data, the Normal Distribution | PDF"]