{"id":5317,"date":"2022-08-19T17:27:28","date_gmt":"2022-08-19T17:27:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5317"},"modified":"2022-08-24T04:08:58","modified_gmt":"2022-08-24T04:08:58","slug":"12a-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/12a-coreq\/","title":{"raw":"12A Coreq","rendered":"12A Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to calculate and\u00a0 interpret z-scores and use a data analysis tool to calculate normal probabilities.\r\n

Calculating and Interpreting z-scores\u00a0<\/strong><\/p>\r\nData collected by the Centers for Disease Control and Prevention show that the\u00a0 average birthweight for babies in the United States is 7.17 pounds and the standard\u00a0 deviation of birthweights is 1.30 pounds.[footnote]Centers for Disease Control and Prevention. (n.d.). Natality for 2016\u20132019 (expanded).\u00a0 https:\/\/wonder.cdc.gov\/controller\/datarequest\/D149;jsessionid=7AB7525C7DC02FF1F19D38C125AC[\/footnote]\r\n

\r\n

Question 1<\/h3>\r\n1) What birthweight is one standard deviation above the mean? What birthweight is one standard deviation below the mean?\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\n2) For each of the two answers you computed in Question 1, subtract the mean of 7.17\u00a0 and then divide by the standard deviation of 1.30. In other words, calculate the\u00a0 following for each birthweight value computed in Question 1:\r\n

Value \u2212 7.17<\/p>\r\n

1.30<\/p>\r\n\r\n<\/div>\r\n

\r\n

Question 3<\/h3>\r\n3) What birthweight is two standard deviations above the mean? What birthweight is\u00a0 two standard deviations below the mean?\r\n\r\n<\/div>\r\n
\r\n

Question 4<\/h3>\r\n4) For each of the two answers you computed in Question 3, subtract the mean of 7.17\u00a0 and then divide by the standard deviation of 1.30. In other words, calculate the\u00a0 following for each birthweight value computed in Question 3:\r\n

Value \u2212 7.17<\/p>\r\n

1.30<\/p>\r\n\r\n<\/div>\r\nThe values you calculated in Questions 2 and 4 are called z-scores or standardized\u00a0 scores. A z-score measures a value\u2019s distance from the mean in units of standard\u00a0 deviation. A positive z-score indicates the value is above the mean, whereas a negative\u00a0 z-score indicates the value is below the mean.\r\n

\r\n

Question 5<\/h3>\r\n5) What birthweight is 1.5 standard deviations below the mean? In other words, what\u00a0 birthweight has a z-score of \u22121.5?\r\n\r\n<\/div>\r\n
\r\n

Question 6<\/h3>\r\n6) A baby is classified as low birthweight if they weigh less than 5.5 pounds.[footnote]2 Martin, J. A., Hamilton, B. E., Osterman, M. J. K., & Driscoll, A. K. (2021, March 23). Births: Final data\u00a0 for 2019. National Vital Statistics Reports, 70(2), 1\u201350.\u00a0https:\/\/www.cdc.gov\/nchs\/data\/nvsr\/nvsr70\/nvsr70-02-508.pdf\u00a0[\/footnote] How\u00a0 many standard deviations from the mean is 5.5 pounds?\r\n\r\n<\/div>\r\n
\r\n

Question 7<\/h3>\r\n7) The Guinness Book of World Records reports that the heaviest baby ever recorded\u00a0 weighed a massive 22 pounds![footnote]Guinness World Records. (n.d.). Heaviest birth. https:\/\/www.guinnessworldrecords.com\/world records\/heaviest-birth[\/footnote] How many standard deviations from the mean is\u00a0 this birthweight?\r\n\r\n<\/div>\r\n

Probabilities as Areas Under the Normal Curve\u00a0<\/strong><\/p>\r\n\r\n

\r\n

Question 8<\/h3>\r\n8) In statistics, you are often interested in finding probabilities involving a normal distribution. These probabilities are calculated by finding the area under a normal\u00a0 curve. Answer the following questions as a review.\r\n\r\na) What is the area under the entire normal curve?\r\n\r\nb) What is the area under the normal curve to the left of the mean?\r\n\r\nc) Suppose you know that the area to the left of a given z-score is 0.32. What is\u00a0 the area to the right of that z-score?\r\n\r\n<\/div>","rendered":"

In the next preview assignment and in the next class, you will need to calculate and\u00a0 interpret z-scores and use a data analysis tool to calculate normal probabilities.<\/p>\n

Calculating and Interpreting z-scores\u00a0<\/strong><\/p>\n

Data collected by the Centers for Disease Control and Prevention show that the\u00a0 average birthweight for babies in the United States is 7.17 pounds and the standard\u00a0 deviation of birthweights is 1.30 pounds.[1]<\/sup><\/a><\/p>\n

\n

Question 1<\/h3>\n

1) What birthweight is one standard deviation above the mean? What birthweight is one standard deviation below the mean?<\/p>\n<\/div>\n

\n

Question 2<\/h3>\n

2) For each of the two answers you computed in Question 1, subtract the mean of 7.17\u00a0 and then divide by the standard deviation of 1.30. In other words, calculate the\u00a0 following for each birthweight value computed in Question 1:<\/p>\n

Value \u2212 7.17<\/p>\n

1.30<\/p>\n<\/div>\n

\n

Question 3<\/h3>\n

3) What birthweight is two standard deviations above the mean? What birthweight is\u00a0 two standard deviations below the mean?<\/p>\n<\/div>\n

\n

Question 4<\/h3>\n

4) For each of the two answers you computed in Question 3, subtract the mean of 7.17\u00a0 and then divide by the standard deviation of 1.30. In other words, calculate the\u00a0 following for each birthweight value computed in Question 3:<\/p>\n

Value \u2212 7.17<\/p>\n

1.30<\/p>\n<\/div>\n

The values you calculated in Questions 2 and 4 are called z-scores or standardized\u00a0 scores. A z-score measures a value\u2019s distance from the mean in units of standard\u00a0 deviation. A positive z-score indicates the value is above the mean, whereas a negative\u00a0 z-score indicates the value is below the mean.<\/p>\n

\n

Question 5<\/h3>\n

5) What birthweight is 1.5 standard deviations below the mean? In other words, what\u00a0 birthweight has a z-score of \u22121.5?<\/p>\n<\/div>\n

\n

Question 6<\/h3>\n

6) A baby is classified as low birthweight if they weigh less than 5.5 pounds.[2]<\/sup><\/a> How\u00a0 many standard deviations from the mean is 5.5 pounds?<\/p>\n<\/div>\n

\n

Question 7<\/h3>\n

7) The Guinness Book of World Records reports that the heaviest baby ever recorded\u00a0 weighed a massive 22 pounds![3]<\/sup><\/a> How many standard deviations from the mean is\u00a0 this birthweight?<\/p>\n<\/div>\n

Probabilities as Areas Under the Normal Curve\u00a0<\/strong><\/p>\n

\n

Question 8<\/h3>\n

8) In statistics, you are often interested in finding probabilities involving a normal distribution. These probabilities are calculated by finding the area under a normal\u00a0 curve. Answer the following questions as a review.<\/p>\n

a) What is the area under the entire normal curve?<\/p>\n

b) What is the area under the normal curve to the left of the mean?<\/p>\n

c) Suppose you know that the area to the left of a given z-score is 0.32. What is\u00a0 the area to the right of that z-score?<\/p>\n<\/div>\n

  1. Centers for Disease Control and Prevention. (n.d.). Natality for 2016\u20132019 (expanded).\u00a0 https:\/\/wonder.cdc.gov\/controller\/datarequest\/D149;jsessionid=7AB7525C7DC02FF1F19D38C125AC ↵<\/a><\/li>
  2. 2 Martin, J. A., Hamilton, B. E., Osterman, M. J. K., & Driscoll, A. K. (2021, March 23). Births: Final data\u00a0 for 2019. National Vital Statistics Reports, 70(2), 1\u201350.\u00a0https:\/\/www.cdc.gov\/nchs\/data\/nvsr\/nvsr70\/nvsr70-02-508.pdf\u00a0 ↵<\/a><\/li>
  3. Guinness World Records. (n.d.). Heaviest birth. https:\/\/www.guinnessworldrecords.com\/world records\/heaviest-birth ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5317","chapter","type-chapter","status-publish","hentry"],"part":5315,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5317","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5317\/revisions"}],"predecessor-version":[{"id":5447,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5317\/revisions\/5447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5315"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5317\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5317"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5317"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5317"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}