{"id":588,"date":"2020-07-20T21:01:07","date_gmt":"2020-07-21T01:01:07","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=part&#038;p=588"},"modified":"2024-02-08T13:31:17","modified_gmt":"2024-02-08T18:31:17","slug":"chapter-5-normal-distribution","status":"publish","type":"part","link":"https:\/\/openbooks.macewan.ca\/introstats\/part\/chapter-5-normal-distribution\/","title":{"raw":"Chapter 5: The Normal Distribution","rendered":"Chapter 5: The Normal Distribution"},"content":{"raw":"<h2>Overview<\/h2>\r\nA random variable can be either discrete or continuous. As mentioned in Chapter 4, a discrete random variable can be described by a probability distribution that lists all the possible values of the random variable and their corresponding probabilities. For a continuous random variable, however, we cannot list all the possible values, so a different approach is required to describe the probability distribution. The so-called density curve describes the probability distribution of a continuous random variable<strong>,<\/strong> and the area under the curve describes probabilities related to continuous random variables. This chapter introduces the normal distribution, one of the most important continuous distributions.\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">Learning Objectives<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAs a result of completing this chapter, you will be able to do the following:\r\n<ul>\r\n \t<li>Describe the properties of a normal density curve.<\/li>\r\n \t<li>Describe the standard normal distribution.<\/li>\r\n \t<li>Use the standard normal table (Table II) in order to:\r\n<ul>\r\n \t<li>Determine the area bounded by some given values under any normal density curve.<\/li>\r\n \t<li>Find values that correspond to given areas under any normal density curve.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Use a normal probability plot to assess whether a given data set seems to come from a normal population.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<h2>Overview<\/h2>\n<p>A random variable can be either discrete or continuous. As mentioned in Chapter 4, a discrete random variable can be described by a probability distribution that lists all the possible values of the random variable and their corresponding probabilities. For a continuous random variable, however, we cannot list all the possible values, so a different approach is required to describe the probability distribution. The so-called density curve describes the probability distribution of a continuous random variable<strong>,<\/strong> and the area under the curve describes probabilities related to continuous random variables. This chapter introduces the normal distribution, one of the most important continuous distributions.<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">Learning Objectives<\/header>\n<div class=\"textbox__content\">\n<p>As a result of completing this chapter, you will be able to do the following:<\/p>\n<ul>\n<li>Describe the properties of a normal density curve.<\/li>\n<li>Describe the standard normal distribution.<\/li>\n<li>Use the standard normal table (Table II) in order to:\n<ul>\n<li>Determine the area bounded by some given values under any normal density curve.<\/li>\n<li>Find values that correspond to given areas under any normal density curve.<\/li>\n<\/ul>\n<\/li>\n<li>Use a normal probability plot to assess whether a given data set seems to come from a normal population.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":5,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-588","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/588","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":7,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/588\/revisions"}],"predecessor-version":[{"id":4754,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/588\/revisions\/4754"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=588"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=588"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=588"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}