{"id":1875,"date":"2024-05-29T09:50:50","date_gmt":"2024-05-29T13:50:50","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=1875"},"modified":"2024-06-12T14:50:45","modified_gmt":"2024-06-12T18:50:45","slug":"using-excels-expon-dist-function","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/using-excels-expon-dist-function\/","title":{"raw":"Using Excel's EXPON.DIST Function","rendered":"Using Excel&#8217;s EXPON.DIST Function"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nUse Excel's EXPON.DIST() function to calculate probabilities of times between events.\r\n\r\n<\/div>\r\n<\/div>\r\nTo calculate the probability of certain times between events, we can use Excel:\r\n<ul>\r\n \t<li>[latex]P(\\text{at most or less than}) =\\text{EXPON.DIST}(x, \\lambda, \\text{TRUE})[\/latex]<\/li>\r\n \t<li>[latex]P(\\text{at least or more than}) =1-\\text{EXPON.DIST}(x, \\lambda, \\text{TRUE})[\/latex]<\/li>\r\n<\/ul>\r\nIn this section, we will revisit the examples from the <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/using-the-exponential-distribution-formulas\/\">previous section<\/a> but use Excel to solve them.\r\n<h1>Calculating the probability of AT Most (EXAMPLE)<\/h1>\r\nWe will revisit the first example from the previous section:\r\n<h2>Example 38.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: A supermarket records the customer arrivals at the check-outs and finds:\r\n<ul>\r\n \t<li>The time between customer arrivals follows an Exponential distribution.<\/li>\r\n \t<li>The time between customer arrivals is, on average, 30 seconds.<\/li>\r\n<\/ul>\r\n<span style=\"color: #003366\"><strong>Question<\/strong><\/span>: What is the probability that a customer will arrive in the next minute at the check-out?\r\n\r\n<span style=\"color: #003366\"><strong>Solution:<\/strong><\/span> Let us use the 'at most' formula and follow the steps below:\r\n<ul>\r\n \t<li><span style=\"color: #003366\">Formula<\/span>: [latex]P(\\text{at most or less than}) =\\text{EXPON.DIST}(x, \\lambda, \\text{TRUE})[\/latex]<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li><span style=\"color: #003366\">Time units<\/span>: minutes<\/li>\r\n \t<li><span style=\"color: #003366\">Lambda<\/span>: [latex]\\lambda = \\frac{1}{30 \\text{ seconds}} \\times \\frac{60 \\text{ seconds}}{1 \\text{ minute}}=2 \\text{ } \\frac{\\text{customers}}{\\text{per minute}}[\/latex]<\/li>\r\n \t<li><span style=\"color: #003366\">X-values<\/span>: [latex]P(\\text{at most 1}) = P(x \\le 1)[\/latex]<\/li>\r\n \t<li><span style=\"color: #003366\">Cumulative<\/span>: TRUE. We always use [latex]\\text{Cumulative} = \\text{TRUE}[\/latex] for exponential distributions. Using [latex]\\text{Cumulative} = \\text{FALSE}[\/latex] gives another function called the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Exponential_distribution\">PDF<\/a> (that we do not need in our calculations).<\/li>\r\n \t<li><span style=\"color: #003366\">Complement?<\/span>\u00a0No. EXPON.DIST() calculates the probability to the left of (or up to and including) the [latex]x[\/latex]-value inputted - which is what we are looking for in this example. We only need to take a complement when calculating the area to the right of the [latex]x[\/latex]-value.<\/li>\r\n \t<li><span style=\"color: #003366\">Answer<\/span>: [latex]P(x \\le 1) = \\text{EXPON.DIST}(1, 2, \\text{TRUE})\u00a0= 0.8647[\/latex]<\/li>\r\n \t<li><span style=\"color: #003366\">Excel File<\/span>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example_38-1.xlsx\">Click here<\/a>\u00a0to download the Excel file with this solution.<\/li>\r\n<\/ul>\r\n<span style=\"color: #003366\"><strong>Conclusion:<\/strong><\/span> There is an 86.47% chance that a customer will arrive in the next minute.\r\n<h1>Calculating the probability of At least (VIDEO)<\/h1>\r\nNext, we will revisit the second example from the previous section:\r\n<h2>Example 38.2.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: The times it takes call center specialist to resolve incoming calls to their call center:\r\n<ul>\r\n \t<li>Follow an exponential distribution.<\/li>\r\n \t<li>Have an average of 2.5 minutes.<\/li>\r\n<\/ul>\r\n<span style=\"color: #003366\"><strong>Question:<\/strong><\/span> What is the probability that a call lasts at least 5 minutes?\r\n\r\nSolution: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example_38-2.xlsx\">Click here<\/a>\u00a0to download the Excel solutions shown in the video below:\r\n\r\nhttps:\/\/youtu.be\/nEJVN2QWnww\r\n<h1>Applying the Memoryless Property (Exercise)<\/h1>\r\nFinally, let's revisit previous example (it's also the same as the last example from the previous section):\r\n<h2>Example 38.2.2<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: We will revisit our previous example...\r\n<ul>\r\n \t<li>The times it takes call center specialist to resolve incoming calls follow an exponential distribution.<\/li>\r\n \t<li>On average, it takes the specialist 2.5 minutes to resolve a call.<\/li>\r\n \t<li>After 5 minutes of being on a call, a warning pops up on the specialist's computer urging them to wrap up the phone call.<\/li>\r\n<\/ul>\r\n<span style=\"color: #003366\"><strong>Question:<\/strong> <\/span>What is the probability, after receiving the warning, that it takes at least another 5 minutes to wrap up the call?\r\n\r\n<span style=\"color: #003366\"><strong>You Try:<\/strong><\/span> Complete the exercise below to solve the above problem:\r\n\r\n[h5p id=\"106\"]\r\n\r\n<span style=\"color: #003366\"><strong>Solution:<\/strong><\/span> <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example_38-2-2.xlsx\">Click here<\/a> to download the Excel file that contains the solution to the above exercise.\r\n\r\n<span style=\"color: #003366\"><strong>Conclusion: <\/strong><\/span>There is 13.53% chance that the call will take at least another 5 minutes to resolve.\r\n<h1>Key Takeaways (EXERCISE)<\/h1>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways: Using Excel's EXPON.DIST Function<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"109\"]\r\n\r\n[h5p id=\"110\"]\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Your Own Notes (EXERCISE)<\/h1>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"16\"]","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Use Excel&#8217;s EXPON.DIST() function to calculate probabilities of times between events.<\/p>\n<\/div>\n<\/div>\n<p>To calculate the probability of certain times between events, we can use Excel:<\/p>\n<ul>\n<li>[latex]P(\\text{at most or less than}) =\\text{EXPON.DIST}(x, \\lambda, \\text{TRUE})[\/latex]<\/li>\n<li>[latex]P(\\text{at least or more than}) =1-\\text{EXPON.DIST}(x, \\lambda, \\text{TRUE})[\/latex]<\/li>\n<\/ul>\n<p>In this section, we will revisit the examples from the <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/using-the-exponential-distribution-formulas\/\">previous section<\/a> but use Excel to solve them.<\/p>\n<h1>Calculating the probability of AT Most (EXAMPLE)<\/h1>\n<p>We will revisit the first example from the previous section:<\/p>\n<h2>Example 38.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: A supermarket records the customer arrivals at the check-outs and finds:<\/p>\n<ul>\n<li>The time between customer arrivals follows an Exponential distribution.<\/li>\n<li>The time between customer arrivals is, on average, 30 seconds.<\/li>\n<\/ul>\n<p><span style=\"color: #003366\"><strong>Question<\/strong><\/span>: What is the probability that a customer will arrive in the next minute at the check-out?<\/p>\n<p><span style=\"color: #003366\"><strong>Solution:<\/strong><\/span> Let us use the &#8216;at most&#8217; formula and follow the steps below:<\/p>\n<ul>\n<li><span style=\"color: #003366\">Formula<\/span>: [latex]P(\\text{at most or less than}) =\\text{EXPON.DIST}(x, \\lambda, \\text{TRUE})[\/latex]<\/li>\n<\/ul>\n<ul>\n<li><span style=\"color: #003366\">Time units<\/span>: minutes<\/li>\n<li><span style=\"color: #003366\">Lambda<\/span>: [latex]\\lambda = \\frac{1}{30 \\text{ seconds}} \\times \\frac{60 \\text{ seconds}}{1 \\text{ minute}}=2 \\text{ } \\frac{\\text{customers}}{\\text{per minute}}[\/latex]<\/li>\n<li><span style=\"color: #003366\">X-values<\/span>: [latex]P(\\text{at most 1}) = P(x \\le 1)[\/latex]<\/li>\n<li><span style=\"color: #003366\">Cumulative<\/span>: TRUE. We always use [latex]\\text{Cumulative} = \\text{TRUE}[\/latex] for exponential distributions. Using [latex]\\text{Cumulative} = \\text{FALSE}[\/latex] gives another function called the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Exponential_distribution\">PDF<\/a> (that we do not need in our calculations).<\/li>\n<li><span style=\"color: #003366\">Complement?<\/span>\u00a0No. EXPON.DIST() calculates the probability to the left of (or up to and including) the [latex]x[\/latex]-value inputted &#8211; which is what we are looking for in this example. We only need to take a complement when calculating the area to the right of the [latex]x[\/latex]-value.<\/li>\n<li><span style=\"color: #003366\">Answer<\/span>: [latex]P(x \\le 1) = \\text{EXPON.DIST}(1, 2, \\text{TRUE})\u00a0= 0.8647[\/latex]<\/li>\n<li><span style=\"color: #003366\">Excel File<\/span>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example_38-1.xlsx\">Click here<\/a>\u00a0to download the Excel file with this solution.<\/li>\n<\/ul>\n<p><span style=\"color: #003366\"><strong>Conclusion:<\/strong><\/span> There is an 86.47% chance that a customer will arrive in the next minute.<\/p>\n<h1>Calculating the probability of At least (VIDEO)<\/h1>\n<p>Next, we will revisit the second example from the previous section:<\/p>\n<h2>Example 38.2.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: The times it takes call center specialist to resolve incoming calls to their call center:<\/p>\n<ul>\n<li>Follow an exponential distribution.<\/li>\n<li>Have an average of 2.5 minutes.<\/li>\n<\/ul>\n<p><span style=\"color: #003366\"><strong>Question:<\/strong><\/span> What is the probability that a call lasts at least 5 minutes?<\/p>\n<p>Solution: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example_38-2.xlsx\">Click here<\/a>\u00a0to download the Excel solutions shown in the video below:<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"How to use Excel&#39;s EXPON.DIST() function to calculate the probability for exponential distributions.\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/nEJVN2QWnww?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h1>Applying the Memoryless Property (Exercise)<\/h1>\n<p>Finally, let&#8217;s revisit previous example (it&#8217;s also the same as the last example from the previous section):<\/p>\n<h2>Example 38.2.2<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: We will revisit our previous example&#8230;<\/p>\n<ul>\n<li>The times it takes call center specialist to resolve incoming calls follow an exponential distribution.<\/li>\n<li>On average, it takes the specialist 2.5 minutes to resolve a call.<\/li>\n<li>After 5 minutes of being on a call, a warning pops up on the specialist&#8217;s computer urging them to wrap up the phone call.<\/li>\n<\/ul>\n<p><span style=\"color: #003366\"><strong>Question:<\/strong> <\/span>What is the probability, after receiving the warning, that it takes at least another 5 minutes to wrap up the call?<\/p>\n<p><span style=\"color: #003366\"><strong>You Try:<\/strong><\/span> Complete the exercise below to solve the above problem:<\/p>\n<div id=\"h5p-106\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-106\" class=\"h5p-iframe\" data-content-id=\"106\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Example 38.2.2 \u2013 Exponential - Using Excel - At Least\"><\/iframe><\/div>\n<\/div>\n<p><span style=\"color: #003366\"><strong>Solution:<\/strong><\/span> <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example_38-2-2.xlsx\">Click here<\/a> to download the Excel file that contains the solution to the above exercise.<\/p>\n<p><span style=\"color: #003366\"><strong>Conclusion: <\/strong><\/span>There is 13.53% chance that the call will take at least another 5 minutes to resolve.<\/p>\n<h1>Key Takeaways (EXERCISE)<\/h1>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways: Using Excel&#8217;s EXPON.DIST Function<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-109\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-109\" class=\"h5p-iframe\" data-content-id=\"109\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Using Excel\u2019s EXPON.DIST Function Key Takeaways\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-110\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-110\" class=\"h5p-iframe\" data-content-id=\"110\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Using Excel\u2019s EXPON.DIST Function Key Takeaways Solutions\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Your Own Notes (EXERCISE)<\/h1>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-16\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-16\" class=\"h5p-iframe\" data-content-id=\"16\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n","protected":false},"author":865,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1875","chapter","type-chapter","status-publish","hentry"],"part":1820,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1875","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1875\/revisions"}],"predecessor-version":[{"id":1966,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1875\/revisions\/1966"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/1820"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1875\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=1875"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1875"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=1875"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=1875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}