{"id":489,"date":"2022-07-11T19:37:42","date_gmt":"2022-07-11T19:37:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=489"},"modified":"2022-07-11T19:37:43","modified_gmt":"2022-07-11T19:37:43","slug":"z-score-and-the-empirical-rule-background-youll-need-4","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/z-score-and-the-empirical-rule-background-youll-need-4\/","title":{"raw":"Z-Score and the Empirical Rule: Background You'll Need 4","rendered":"Z-Score and the Empirical Rule: Background You’ll Need 4"},"content":{"raw":"Now let's spend some time understanding how and in what way these kinds of calculations can go wrong.\r\n

Identifying Calculation Mistakes<\/h3>\r\nSuppose the statistician making these calculations thought she was using her calculator correctly, but in three different attempts, she arrived at three different answers. The three potential answers to her computational problem are shown below in Questions 9, 10, and 11 rounded to the nearest hundredth. For each, decide if it was computed correctly or, if not, explain what went wrong. Please refer to the Order of Operations<\/a> Student Resource as needed.\r\n
\r\n

Interactive example<\/h3>\r\nWhen making complicated calculations involving order of operations, your calculator can be a friend or a foe. Some of the most commonly occurring mistakes come from not using parentheses to wrap up operations that need to occur first. Dropped negatives and mislabeled units are also common culprits. You'll be presented with questions below that may include any of these tricky spots. Let's practice a bit before moving on.\r\n\r\nBoth of the questions below have mistakes. What are they?\r\n
    \r\n \t
  1. [latex]\\dfrac{15-12}{4}=12[\/latex]<\/li>\r\n \t
  2. [latex]\\dfrac{7-9}{8}=\\dfrac{1}{4}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"51189\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"51189\"]\r\n
      \r\n \t
    1. The answer should be [latex]0.75[\/latex] or [latex]\\dfrac{1}{4}[\/latex]. Order of operations was not followed. It looks like it was typed into a calculator as [latex]15-12\\text{ \/}4[\/latex], which the calculator interpreted as [latex]15 - \\dfrac{12}{4}[\/latex].<\/li>\r\n \t
    2. The answer should be [latex]-\\dfrac{1}{4}[\/latex] or [latex]-0.25[\/latex]. Either a negative was dropped or the [latex]7[\/latex] was subtracted from the [latex]9[\/latex] by mistake.<\/li>\r\n<\/ol>\r\nDid you recognize a situation in which you tend to make mistakes? Everyone has them -- favorite mistakes -- even math teachers! The key is to recognize them and put up a mental red flag when you encounter those situations, then slow down and handle the calculation carefully.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn to try finding the mistakes. Some of the questions below may have a mistake, and some may not.\r\n
      \r\n

      question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]241200[\/ohm_question]\r\n\r\n[reveal-answer q=\"923550\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"923550\"]Consider how order of operations may have gone wrong.[\/hidden-answer]\r\n\r\n<\/div>\r\n
      \r\n

      question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]241201[\/ohm_question]\r\n\r\n[reveal-answer q=\"653940\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"653940\"]Should this answer be negative or positive?[\/hidden-answer]\r\n\r\n<\/div>\r\n
      \r\n

      question 11<\/h3>\r\n[ohm_question hide_question_numbers=1]241202[\/ohm_question]\r\n\r\n[reveal-answer q=\"122468\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"122468\"]Does this answer appear to be incorrect?[\/hidden-answer]\r\n\r\n<\/div>\r\nQuestions 12, 13, and 14 below show three potential answers to a similar computational problem, rounded to the nearest hundredth. This time, the units of measure are included. For each, decide if it was computed correctly or, if not, explain what went wrong.\r\n
      \r\n

      question 12<\/h3>\r\n[ohm_question hide_question_numbers=1]241203[\/ohm_question]\r\n\r\n[reveal-answer q=\"362651\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"362651\"]Does this answer appear to be incorrect?[\/hidden-answer]\r\n\r\n<\/div>\r\n
      \r\n

      question 13<\/h3>\r\n[ohm_question hide_question_numbers=1]241204[\/ohm_question]\r\n\r\n[reveal-answer q=\"409560\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"409560\"]Should this answer be positive or negative?[\/hidden-answer]\r\n\r\n<\/div>\r\n
      \r\n

      question 14<\/h3>\r\n[ohm_question hide_question_numbers=1]241206[\/ohm_question]\r\n\r\n[reveal-answer q=\"281788\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"281788\"]Should the units cancel out? What units should the answer be in? [\/hidden-answer]\r\n\r\n<\/div>\r\nNow that you've had some practice making these calculations and learning how they can go wrong, it's time to move on to the next section.\r\n\r\n ","rendered":"

      Now let’s spend some time understanding how and in what way these kinds of calculations can go wrong.<\/p>\n

      Identifying Calculation Mistakes<\/h3>\n

      Suppose the statistician making these calculations thought she was using her calculator correctly, but in three different attempts, she arrived at three different answers. The three potential answers to her computational problem are shown below in Questions 9, 10, and 11 rounded to the nearest hundredth. For each, decide if it was computed correctly or, if not, explain what went wrong. Please refer to the Order of Operations<\/a> Student Resource as needed.<\/p>\n

      \n

      Interactive example<\/h3>\n

      When making complicated calculations involving order of operations, your calculator can be a friend or a foe. Some of the most commonly occurring mistakes come from not using parentheses to wrap up operations that need to occur first. Dropped negatives and mislabeled units are also common culprits. You’ll be presented with questions below that may include any of these tricky spots. Let’s practice a bit before moving on.<\/p>\n

      Both of the questions below have mistakes. What are they?<\/p>\n

        \n
      1. [latex]\\dfrac{15-12}{4}=12[\/latex]<\/li>\n
      2. [latex]\\dfrac{7-9}{8}=\\dfrac{1}{4}[\/latex]<\/li>\n<\/ol>\n
        Show Answer<\/span><\/p>\n
        \n
          \n
        1. The answer should be [latex]0.75[\/latex] or [latex]\\dfrac{1}{4}[\/latex]. Order of operations was not followed. It looks like it was typed into a calculator as [latex]15-12\\text{ \/}4[\/latex], which the calculator interpreted as [latex]15 - \\dfrac{12}{4}[\/latex].<\/li>\n
        2. The answer should be [latex]-\\dfrac{1}{4}[\/latex] or [latex]-0.25[\/latex]. Either a negative was dropped or the [latex]7[\/latex] was subtracted from the [latex]9[\/latex] by mistake.<\/li>\n<\/ol>\n

          Did you recognize a situation in which you tend to make mistakes? Everyone has them — favorite mistakes — even math teachers! The key is to recognize them and put up a mental red flag when you encounter those situations, then slow down and handle the calculation carefully.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

          Now it’s your turn to try finding the mistakes. Some of the questions below may have a mistake, and some may not.<\/p>\n

          \n

          question 9<\/h3>\n