{"id":512,"date":"2022-07-11T19:47:20","date_gmt":"2022-07-11T19:47:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=512"},"modified":"2022-07-11T19:47:20","modified_gmt":"2022-07-11T19:47:20","slug":"z-score-and-the-empirical-rule-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/z-score-and-the-empirical-rule-learn-it-4\/","title":{"raw":"Z-Score and the Empirical Rule: Learn It 4","rendered":"Z-Score and the Empirical Rule: Learn It 4"},"content":{"raw":"

The Empirical Rule<\/h2>\r\nIf a distribution is bell shaped, unimodal, and symmetric, then we can estimate how many observations are within a certain number of standard deviations. The Empirical Rule<\/strong> (also known as the\u00a0[latex]68-95-99.7[\/latex] rule) is a guideline that predicts the percentage of observations within a certain number of standard deviations.\r\n
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the empirical rule<\/h3>\r\n[insert a video describing (but not using) the Empirical Rule]-->this video could be good, but she refers back to other lessons and writes on the diagram in a way that could be confusing (calculating half of 68% and not others, uses x bar and s instead of mu and sigma, writes 99.7% on the outside of the bell while the others are clearly written inside). She begins an example at 4:41.<\/span>\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=1AmZjyXKveM[\/embed]\r\n\r\n<\/div>\r\nThe Empirical Rule states that:\r\n
    \r\n \t
  • about\u00a0[latex]68[\/latex]% of observations in a data set will be within one standard deviation of the mean.<\/li>\r\n \t
  • about\u00a0[latex]95[\/latex]% of the observations in a data set will be within two standard deviations of the mean.<\/li>\r\n \t
  • about\u00a0[latex]99.7[\/latex]% of the observations in a data set will be within three standard deviations of the mean.<\/li>\r\n<\/ul>\r\nGraphically, the Empirical Rule can be expressed like this:\r\n\r\n\"A<\/strong>\r\n\r\nFill in the blank for each of\u00a0Questions 10 - 12\r\n
    \r\n

    question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]241220[\/ohm_question]\r\n\r\n[reveal-answer q=\"495115\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"495115\"]Use the image and definition above. [\/hidden-answer]\r\n\r\n<\/div>\r\n
    \r\n

    question 11<\/h3>\r\n[ohm_question hide_question_numbers=1]241225[\/ohm_question]\r\n\r\n[reveal-answer q=\"532094\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"532094\"]Use the image and definition above.[\/hidden-answer]\r\n\r\n<\/div>\r\n
    \r\n

    question 12<\/h3>\r\n[ohm_question hide_question_numbers=1]241227[\/ohm_question]\r\n\r\n[reveal-answer q=\"820605\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"820605\"]Use the image and definition above.[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

    The Empirical Rule<\/h2>\n

    If a distribution is bell shaped, unimodal, and symmetric, then we can estimate how many observations are within a certain number of standard deviations. The Empirical Rule<\/strong> (also known as the\u00a0[latex]68-95-99.7[\/latex] rule) is a guideline that predicts the percentage of observations within a certain number of standard deviations.<\/p>\n

    \n

    the empirical rule<\/h3>\n

    [insert a video describing (but not using) the Empirical Rule]–>this video could be good, but she refers back to other lessons and writes on the diagram in a way that could be confusing (calculating half of 68% and not others, uses x bar and s instead of mu and sigma, writes 99.7% on the outside of the bell while the others are clearly written inside). She begins an example at 4:41.<\/span><\/p>\n