{"id":255776,"date":"2025-07-13T09:02:10","date_gmt":"2025-07-13T09:02:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=255776"},"modified":"2025-07-13T09:02:12","modified_gmt":"2025-07-13T09:02:12","slug":"the-bureau-of-transportation-statistics-reports-on-time-performance-for-airlines-at-ma-jor-airports_-jetblue-united-and-us-airways-share-terminal-e-at-bostons-logan-airport","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/13\/the-bureau-of-transportation-statistics-reports-on-time-performance-for-airlines-at-ma-jor-airports_-jetblue-united-and-us-airways-share-terminal-e-at-bostons-logan-airport\/","title":{"rendered":"The Bureau of Transportation Statistics reports On-time performance for airlines at ma- jor airports_ JetBlue United, and US Airways share terminal \u20ac at Boston&#8217;s Logan Airport"},"content":{"rendered":"\n<p>The Bureau of Transportation Statistics reports On-time performance for airlines at ma- jor airports_ JetBlue United, and US Airways share terminal \u20ac at Boston&#8217;s Logan Airport. Suppose that the Percentage of on-time flights reported was 76.8% for JetBlue; 71.5% for United and 82.27 for US Airways_ Assume that 307 of flights arriving at terminal arc JetBlue flights; 32% are United Flights, and 38% are US Airways Flights. a) Develop joint probability table with threc rows (the airlines) and two columns (on timc status)_ Round the the fourth decimal place b) An announcement is made that Flight 1382 will arriving at gate 20 of terminal C. What is the probability that Flight 1382 will arrive on time? c) What is the most likely airline for Flight 1382? What is the probability that Flight 1382 is by this airline? Suppose that announcement is made saying that Flight 1382 will now be arriving late. What is the most likely airline for this flight? What is the probability that Flight 1382 is by this airline?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s break down the problem step by step:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">a) Joint Probability Table<\/h3>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>JetBlue<\/strong>: 76.8% on-time, 307 flights at the terminal.<\/li>\n\n\n\n<li><strong>United<\/strong>: 71.5% on-time, 32% of flights at the terminal.<\/li>\n\n\n\n<li><strong>US Airways<\/strong>: 82.2% on-time, 38% of flights at the terminal.<\/li>\n<\/ul>\n\n\n\n<p>From the data, we can construct the joint probability table.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Total percentage of flights:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The total percentage of flights at the terminal is 307 for JetBlue, 32% for United, and 38% for US Airways. This gives us the proportions of flights at each airline\u2019s terminal.<\/li>\n\n\n\n<li><strong>P(JetBlue)<\/strong> = 0.307<\/li>\n\n\n\n<li><strong>P(United)<\/strong> = 0.32<\/li>\n\n\n\n<li><strong>P(US Airways)<\/strong> = 0.38<\/li>\n<\/ul>\n\n\n\n<p>Now, for each airline, we need to calculate the probability of on-time and late arrivals.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">JetBlue:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P(On-time | JetBlue)<\/strong> = 0.768<\/li>\n\n\n\n<li><strong>P(Late | JetBlue)<\/strong> = 1 &#8211; 0.768 = 0.232<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">United:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P(On-time | United)<\/strong> = 0.715<\/li>\n\n\n\n<li><strong>P(Late | United)<\/strong> = 1 &#8211; 0.715 = 0.285<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">US Airways:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P(On-time | US Airways)<\/strong> = 0.822<\/li>\n\n\n\n<li><strong>P(Late | US Airways)<\/strong> = 1 &#8211; 0.822 = 0.178<\/li>\n<\/ul>\n\n\n\n<p>We can now calculate the joint probabilities by multiplying the marginal probabilities by the conditional probabilities (on-time or late):P(JetBlue&nbsp;and&nbsp;On-time)=P(JetBlue)\u00d7P(On-time&nbsp;|&nbsp;JetBlue)=0.307\u00d70.768=0.2362\\text{P(JetBlue and On-time)} = P(\\text{JetBlue}) \\times P(\\text{On-time | JetBlue}) = 0.307 \\times 0.768 = 0.2362P(JetBlue&nbsp;and&nbsp;On-time)=P(JetBlue)\u00d7P(On-time&nbsp;|&nbsp;JetBlue)=0.307\u00d70.768=0.2362P(JetBlue&nbsp;and&nbsp;Late)=P(JetBlue)\u00d7P(Late&nbsp;|&nbsp;JetBlue)=0.307\u00d70.232=0.0712\\text{P(JetBlue and Late)} = P(\\text{JetBlue}) \\times P(\\text{Late | JetBlue}) = 0.307 \\times 0.232 = 0.0712P(JetBlue&nbsp;and&nbsp;Late)=P(JetBlue)\u00d7P(Late&nbsp;|&nbsp;JetBlue)=0.307\u00d70.232=0.0712P(United&nbsp;and&nbsp;On-time)=P(United)\u00d7P(On-time&nbsp;|&nbsp;United)=0.32\u00d70.715=0.2288\\text{P(United and On-time)} = P(\\text{United}) \\times P(\\text{On-time | United}) = 0.32 \\times 0.715 = 0.2288P(United&nbsp;and&nbsp;On-time)=P(United)\u00d7P(On-time&nbsp;|&nbsp;United)=0.32\u00d70.715=0.2288P(United&nbsp;and&nbsp;Late)=P(United)\u00d7P(Late&nbsp;|&nbsp;United)=0.32\u00d70.285=0.0912\\text{P(United and Late)} = P(\\text{United}) \\times P(\\text{Late | United}) = 0.32 \\times 0.285 = 0.0912P(United&nbsp;and&nbsp;Late)=P(United)\u00d7P(Late&nbsp;|&nbsp;United)=0.32\u00d70.285=0.0912P(US&nbsp;Airways&nbsp;and&nbsp;On-time)=P(US&nbsp;Airways)\u00d7P(On-time&nbsp;|&nbsp;US&nbsp;Airways)=0.38\u00d70.822=0.3124\\text{P(US Airways and On-time)} = P(\\text{US Airways}) \\times P(\\text{On-time | US Airways}) = 0.38 \\times 0.822 = 0.3124P(US&nbsp;Airways&nbsp;and&nbsp;On-time)=P(US&nbsp;Airways)\u00d7P(On-time&nbsp;|&nbsp;US&nbsp;Airways)=0.38\u00d70.822=0.3124P(US&nbsp;Airways&nbsp;and&nbsp;Late)=P(US&nbsp;Airways)\u00d7P(Late&nbsp;|&nbsp;US&nbsp;Airways)=0.38\u00d70.178=0.0676\\text{P(US Airways and Late)} = P(\\text{US Airways}) \\times P(\\text{Late | US Airways}) = 0.38 \\times 0.178 = 0.0676P(US&nbsp;Airways&nbsp;and&nbsp;Late)=P(US&nbsp;Airways)\u00d7P(Late&nbsp;|&nbsp;US&nbsp;Airways)=0.38\u00d70.178=0.0676<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Joint Probability Table:<\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Airline<\/th><th>On-time (P)<\/th><th>Late (P)<\/th><\/tr><\/thead><tbody><tr><td>JetBlue<\/td><td>0.2362<\/td><td>0.0712<\/td><\/tr><tr><td>United<\/td><td>0.2288<\/td><td>0.0912<\/td><\/tr><tr><td>US Airways<\/td><td>0.3124<\/td><td>0.0676<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">b) Probability that Flight 1382 is on time<\/h3>\n\n\n\n<p>To find the probability that Flight 1382 will arrive on time, we need to use the law of total probability:P(On-time)=P(On-time&nbsp;|&nbsp;JetBlue)\u00d7P(JetBlue)+P(On-time&nbsp;|&nbsp;United)\u00d7P(United)+P(On-time&nbsp;|&nbsp;US&nbsp;Airways)\u00d7P(US&nbsp;Airways)P(\\text{On-time}) = P(\\text{On-time | JetBlue}) \\times P(\\text{JetBlue}) + P(\\text{On-time | United}) \\times P(\\text{United}) + P(\\text{On-time | US Airways}) \\times P(\\text{US Airways})P(On-time)=P(On-time&nbsp;|&nbsp;JetBlue)\u00d7P(JetBlue)+P(On-time&nbsp;|&nbsp;United)\u00d7P(United)+P(On-time&nbsp;|&nbsp;US&nbsp;Airways)\u00d7P(US&nbsp;Airways)<\/p>\n\n\n\n<p>Substitute the values:P(On-time)=(0.768\u00d70.307)+(0.715\u00d70.32)+(0.822\u00d70.38)P(\\text{On-time}) = (0.768 \\times 0.307) + (0.715 \\times 0.32) + (0.822 \\times 0.38)P(On-time)=(0.768\u00d70.307)+(0.715\u00d70.32)+(0.822\u00d70.38)P(On-time)=0.2362+0.2288+0.3124=0.7774P(\\text{On-time}) = 0.2362 + 0.2288 + 0.3124 = 0.7774P(On-time)=0.2362+0.2288+0.3124=0.7774<\/p>\n\n\n\n<p>So, the probability that Flight 1382 will arrive on time is <strong>0.7774<\/strong> or <strong>77.74%<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">c) Most likely airline for Flight 1382 (if on time)<\/h3>\n\n\n\n<p>To determine the most likely airline for Flight 1382 if it arrives on time, we need to find the conditional probabilities using <strong>Bayes&#8217; Theorem<\/strong>.<\/p>\n\n\n\n<p>The conditional probability is given by:P(JetBlue&nbsp;|&nbsp;On-time)=P(JetBlue&nbsp;and&nbsp;On-time)P(On-time)=0.23620.7774=0.303P(\\text{JetBlue | On-time}) = \\frac{P(\\text{JetBlue and On-time})}{P(\\text{On-time})} = \\frac{0.2362}{0.7774} = 0.303P(JetBlue&nbsp;|&nbsp;On-time)=P(On-time)P(JetBlue&nbsp;and&nbsp;On-time)\u200b=0.77740.2362\u200b=0.303P(United&nbsp;|&nbsp;On-time)=P(United&nbsp;and&nbsp;On-time)P(On-time)=0.22880.7774=0.294P(\\text{United | On-time}) = \\frac{P(\\text{United and On-time})}{P(\\text{On-time})} = \\frac{0.2288}{0.7774} = 0.294P(United&nbsp;|&nbsp;On-time)=P(On-time)P(United&nbsp;and&nbsp;On-time)\u200b=0.77740.2288\u200b=0.294P(US&nbsp;Airways&nbsp;|&nbsp;On-time)=P(US&nbsp;Airways&nbsp;and&nbsp;On-time)P(On-time)=0.31240.7774=0.402P(\\text{US Airways | On-time}) = \\frac{P(\\text{US Airways and On-time})}{P(\\text{On-time})} = \\frac{0.3124}{0.7774} = 0.402P(US&nbsp;Airways&nbsp;|&nbsp;On-time)=P(On-time)P(US&nbsp;Airways&nbsp;and&nbsp;On-time)\u200b=0.77740.3124\u200b=0.402<\/p>\n\n\n\n<p>The most likely airline is <strong>US Airways<\/strong>, with a probability of <strong>40.2%<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">d) Most likely airline if Flight 1382 is late<\/h3>\n\n\n\n<p>For the late arrival scenario, we repeat the same steps but with the probabilities of late arrivals.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Conditional probabilities for late flights:<\/h4>\n\n\n\n<p>P(JetBlue&nbsp;|&nbsp;Late)=P(JetBlue&nbsp;and&nbsp;Late)P(Late)=0.07121\u22120.7774=0.07120.2226=0.32P(\\text{JetBlue | Late}) = \\frac{P(\\text{JetBlue and Late})}{P(\\text{Late})} = \\frac{0.0712}{1 &#8211; 0.7774} = \\frac{0.0712}{0.2226} = 0.32P(JetBlue&nbsp;|&nbsp;Late)=P(Late)P(JetBlue&nbsp;and&nbsp;Late)\u200b=1\u22120.77740.0712\u200b=0.22260.0712\u200b=0.32P(United&nbsp;|&nbsp;Late)=P(United&nbsp;and&nbsp;Late)P(Late)=0.09120.2226=0.409P(\\text{United | Late}) = \\frac{P(\\text{United and Late})}{P(\\text{Late})} = \\frac{0.0912}{0.2226} = 0.409P(United&nbsp;|&nbsp;Late)=P(Late)P(United&nbsp;and&nbsp;Late)\u200b=0.22260.0912\u200b=0.409P(US&nbsp;Airways&nbsp;|&nbsp;Late)=P(US&nbsp;Airways&nbsp;and&nbsp;Late)P(Late)=0.06760.2226=0.303P(\\text{US Airways | Late}) = \\frac{P(\\text{US Airways and Late})}{P(\\text{Late})} = \\frac{0.0676}{0.2226} = 0.303P(US&nbsp;Airways&nbsp;|&nbsp;Late)=P(Late)P(US&nbsp;Airways&nbsp;and&nbsp;Late)\u200b=0.22260.0676\u200b=0.303<\/p>\n\n\n\n<p>The most likely airline if Flight 1382 is late is <strong>United<\/strong>, with a probability of <strong>40.9%<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a) The joint probability table has been developed.<\/li>\n\n\n\n<li>b) The probability that Flight 1382 will arrive on time is 77.74%.<\/li>\n\n\n\n<li>c) The most likely airline for Flight 1382 to be on time is <strong>US Airways<\/strong> with a probability of 40.2%.<\/li>\n\n\n\n<li>d) If Flight 1382 is late, the most likely airline is <strong>United<\/strong> with a probability of 40.9%.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-488.jpeg\" alt=\"\" class=\"wp-image-255777\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Bureau of Transportation Statistics reports On-time performance for airlines at ma- jor airports_ JetBlue United, and US Airways share terminal \u20ac at Boston&#8217;s Logan Airport. Suppose that the Percentage of on-time flights reported was 76.8% for JetBlue; 71.5% for United and 82.27 for US Airways_ Assume that 307 of flights arriving at terminal arc [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-255776","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255776","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=255776"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255776\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=255776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=255776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=255776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}